{"48571bf42f9b3e1b94b541f568cd4f0fisw-bibliothek":{"DOI":"10.23919/ECC64448.2024.10591213","ISBN":"","ISSN":"","URL":"","abstract":"Rack-and-pinion drives are commonly used in large machine tools to provide linear motion of heavy loads over long travel distances. A key concern in this context is the achievable path accuracy, which is limited by assembly and manufacturing tolerances of the gearing components in conjunction with load-dependent deformation and the inherent backlash of the system. To address this issue, this paper presents a method for robust modeling of the individual and state-dependent transmission errors of a drive utilizing a two-stage machine learning approach. Based on this, the position control is extended to include an error compensation, which suppresses the modeled deviations in the mechanical system including the position-dependent backlash. The achievable increase in path accuracy as well as the robustness of the approach are evaluated and quantified by an experimental validation on a system with industry standard components.","annote":"","author":[{"family":"Steinle","given":"Lukas"},{"family":"Leipe","given":"Valentin"},{"family":"Lechler","given":"Armin"},{"family":"Veri","given":"Alexander"}],"citation-label":"10591213","collection-editor":[],"collection-title":"","container-author":[],"container-title":"2024 European Control Conference (ECC)","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2024","June"]],"literal":"2024"},"event-place":"","id":"48571bf42f9b3e1b94b541f568cd4f0fisw-bibliothek","interhash":"fc115f1ff8efe474a50ffb3153d44a85","intrahash":"48571bf42f9b3e1b94b541f568cd4f0f","issue":"","issued":{"date-parts":[["2024","June"]],"literal":"2024"},"keyword":"compensation drive error feed isw learning machine tool","misc":{"doi":"10.23919/ECC64448.2024.10591213"},"note":"","number":"","number-of-pages":"6","page":"2441-2447","page-first":"2441","publisher":"","publisher-place":"","status":"","title":"Learning Compensation of the State-Dependent Transmission Errors in Rack-and-Pinion Drives","type":"paper-conference","username":"isw-bibliothek","version":"","volume":""},"ec952595ff449504c1022011ebc3d996tourian":{"DOI":"https://doi.org/10.1029/2022EA002352","ISBN":"","ISSN":"","URL":"https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2022EA002352","abstract":"Abstract European Center for Medium-Range Weather Forecasts Reanalysis (ERA), one of the most widely used precipitation products, has evolved from ERA-40 to ERA-20CM, ERA-20C, ERA-Interim, and ERA5. Studies evaluating the performance of individual ERA products cannot adequately assess the evolution of the products. We compared the performance of all ERA precipitation products at daily, monthly, and annual data (1980–2018) using more than 2100 Iran precipitation gauges. Results indicated that ERA-40 performed worst, followed by ERA-20CM, which showed only minor improvements over ERA-40. ERA-20C considerably outperformed its predecessors, benefiting from the assimilation of observational data. Although several previous studies have reported full superiority of ERA5 over ERA-Interim, our results revealed several shortcomings in ERA5 compared with the ERA-Interim estimates. Both ERA-Interim and ERA5 performed best overall, with ERA-Interim showing better statistical and categorical skill scores, and ERA5 performing better in estimating extreme precipitations. These results suggest that the accuracy of ERA precipitation products has improved from ERA-40 to ERA-Interim, but not consistently from ERA-Interim to ERA5. This study employed a grid-grid comparison approach by first creating a gridded reference data set through the spatial aggregation of point source observations, however, the results from a point-grid approach showed no change in the overall ranking of products (despite the slight changes in the error index values). These findings are useful for model development at a global scale and for hydrological applications in Iran.","annote":"","author":[{"family":"Ghajarnia","given":"Navid"},{"family":"Akbari","given":"Mahdi"},{"family":"Saemian","given":"Peyman"},{"family":"Ehsani","given":"Mohammad Reza"},{"family":"Hosseini-Moghari","given":"Seyed-Mohammad"},{"family":"Azizian","given":"Asghar"},{"family":"Kalantari","given":"Zahra"},{"family":"Behrangi","given":"Ali"},{"family":"Tourian","given":"Mohammad J."},{"family":"Klöve","given":"Björn"},{"family":"Haghighi","given":"Ali Torabi"}],"citation-label":"https://doi.org/10.1029/2022EA002352","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Earth and Space Science","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2022"]],"literal":"2022"},"event-place":"","id":"ec952595ff449504c1022011ebc3d996tourian","interhash":"864577af10785fbb6ed1ad6c31ba06e2","intrahash":"ec952595ff449504c1022011ebc3d996","issue":"10","issued":{"date-parts":[["2022"]],"literal":"2022"},"keyword":"ERA, analysis decomposition, error estimates, evaluation, geoinst imported multi-scale precipitation statistical","misc":{"eprint":"https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2022EA002352","doi":"https://doi.org/10.1029/2022EA002352"},"note":"e2022EA002352 2022EA002352","number":"10","number-of-pages":"330","page":"e2022EA002352","page-first":"2022","publisher":"","publisher-place":"","status":"","title":"Evaluating the Evolution of ECMWF Precipitation Products Using Observational Data for Iran: From ERA40 to ERA5","type":"article-journal","username":"tourian","version":"","volume":"9"},"88e9a857661efa99f399e9d4f24b559emathematik":{"DOI":"10.1016/j.sysconle.2011.10.012","ISBN":"","ISSN":"","URL":"http://dx.doi.org/10.1016/j.sysconle.2011.10.012","abstract":"In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"WH12","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Systems & Control Letters","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"88e9a857661efa99f399e9d4f24b559emathematik","interhash":"e80ae72fe2c1f9f79f4f7f8f5ce00735","intrahash":"88e9a857661efa99f399e9d4f24b559e","issue":"1","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"subspace error dynamical kernel a-posteriori from:britsteiner methods, ians nonlinear systems, offline/online decomposition, projection estimates, model anm reduction,","misc":{"owner":"schmidta","groups":"haasdonk, haasdonk_all_papers","file":":PDF/WH12_www_preprint_error_estimation_nonlinear_kernel_based_reduced_systems.pdf:PDF","doi":"10.1016/j.sysconle.2011.10.012"},"note":"","number":"1","number-of-pages":"8","page":"203--211","page-first":"203","publisher":"Elsevier BV","publisher-place":"","status":"","title":"Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems","type":"article-journal","username":"mathematik","version":"","volume":"61"},"a83ef7da936322ea35f09a4d03bb61bdmathematik":{"DOI":"10.1007/s10444-014-9396-6","ISBN":"","ISSN":"","URL":"http://link.springer.com/article/10.1007/s10444-014-9396-6","abstract":"","annote":"","author":[{"family":"Martini","given":"I."},{"family":"Rozza","given":"G."},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"Maier2014a","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Advances in Computational Mathematics","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2015"]],"literal":"2015"},"event-place":"","id":"a83ef7da936322ea35f09a4d03bb61bdmathematik","interhash":"1474e2e0db6128c1ec02771a5ff8841b","intrahash":"a83ef7da936322ea35f09a4d03bb61bd","issue":"5","issued":{"date-parts":[["2015"]],"literal":"2015"},"keyword":"Error decomposition; medium 76D07 from:britsteiner Porous Reduced ians method; basis problem; Stokes 76S05; estimation; equation; Domain Non-coercive flow; anm 65N55;","misc":{"owner":"maieril","groups":"haasdonk, maieril, haasdonk_all_papers","file":":PDF/Maier2014a_www_RB_stokes_darcy_preprint.pdf:PDF","doi":"10.1007/s10444-014-9396-6"},"note":"","number":"5","number-of-pages":"26","page":"1131--1157","page-first":"1131","publisher":"","publisher-place":"","status":"","title":"Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system","type":"article-journal","username":"mathematik","version":"","volume":"41"},"c9ff784e6a0440b80b45055fa2c9df7ebritsteiner":{"DOI":"","ISBN":"","ISSN":"","URL":"http://www.ifac-papersonline.net/","abstract":"This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"Wirtz2012a","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"c9ff784e6a0440b80b45055fa2c9df7ebritsteiner","interhash":"e6dce191069323c30bda8a87cce2913a","intrahash":"c9ff784e6a0440b80b45055fa2c9df7e","issue":"","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori anm decomposition, dynamical error estimates, ians kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems,","misc":{"owner":"haasdonk","file":":PDF/WH12b_preprint.pdf:PDF","groups":"haasdonk, haasdonk_all_papers"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A-posteriori error estimation for parameterized kernel-based systems","type":"paper-conference","username":"britsteiner","version":"","volume":""},"88e9a857661efa99f399e9d4f24b559ebritsteiner":{"DOI":"10.1016/j.sysconle.2011.10.012","ISBN":"","ISSN":"","URL":"http://dx.doi.org/10.1016/j.sysconle.2011.10.012","abstract":"In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"WH12","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Systems & Control Letters","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"88e9a857661efa99f399e9d4f24b559ebritsteiner","interhash":"e80ae72fe2c1f9f79f4f7f8f5ce00735","intrahash":"88e9a857661efa99f399e9d4f24b559e","issue":"1","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori anm decomposition, dynamical error estimates, ians kernel methods, model nonlinear offline/online projection reduction, subspace systems,","misc":{"owner":"schmidta","groups":"haasdonk, haasdonk_all_papers","file":":PDF/WH12_www_preprint_error_estimation_nonlinear_kernel_based_reduced_systems.pdf:PDF","doi":"10.1016/j.sysconle.2011.10.012"},"note":"","number":"1","number-of-pages":"8","page":"203--211","page-first":"203","publisher":"Elsevier BV","publisher-place":"","status":"","title":"Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems","type":"article-journal","username":"britsteiner","version":"","volume":"61"},"a83ef7da936322ea35f09a4d03bb61bdbritsteiner":{"DOI":"10.1007/s10444-014-9396-6","ISBN":"","ISSN":"","URL":"http://link.springer.com/article/10.1007/s10444-014-9396-6","abstract":"","annote":"","author":[{"family":"Martini","given":"I."},{"family":"Rozza","given":"G."},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"Maier2014a","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Advances in Computational Mathematics","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2015"]],"literal":"2015"},"event-place":"","id":"a83ef7da936322ea35f09a4d03bb61bdbritsteiner","interhash":"1474e2e0db6128c1ec02771a5ff8841b","intrahash":"a83ef7da936322ea35f09a4d03bb61bd","issue":"5","issued":{"date-parts":[["2015"]],"literal":"2015"},"keyword":"65N55; 76D07 76S05; Domain Error Non-coercive Porous Reduced Stokes anm basis decomposition; equation; estimation; flow; ians medium method; problem;","misc":{"owner":"maieril","groups":"haasdonk, maieril, haasdonk_all_papers","file":":PDF/Maier2014a_www_RB_stokes_darcy_preprint.pdf:PDF","doi":"10.1007/s10444-014-9396-6"},"note":"","number":"5","number-of-pages":"26","page":"1131--1157","page-first":"1131","publisher":"","publisher-place":"","status":"","title":"Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system","type":"article-journal","username":"britsteiner","version":"","volume":"41"},"072da899c758affe0d062ab23098b302ingmarkallfass":{"DOI":"10.1109/TMTT.2015.2467390","ISBN":"","ISSN":"","URL":"","abstract":"","annote":"","author":[{"family":"Antes","given":"J."},{"family":"Kallfass","given":"I."}],"citation-label":"Antes_MTT2015-2","collection-editor":[],"collection-title":"","container-author":[],"container-title":"IEEE Trans. on Microwave Theory and Techniques","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2015"]],"literal":"2015"},"event-place":"","id":"072da899c758affe0d062ab23098b302ingmarkallfass","interhash":"a25ee8cd0c744aec557a35e0f991f07e","intrahash":"072da899c758affe0d062ab23098b302","issue":"10","issued":{"date-parts":[["2015"]],"literal":"2015"},"keyword":"(BER);complex (EVM);millimeter-wave (MMICs);performance (SER);wireless (mmw) amplitude bandwidths;in-phase broadband channels;E-band characteristics;performance circuits communication communication;Bit communication;mmw error error;submillimeter-wave estimation;performance estimation;symbol factor;local frequency frontend frontend;broadband imbalance;in-phase imbalance;limiting imbalance;quadrature imperfection;performance integrated keying keying;radio limiting limits;quadrature links;broadband links;channel magnitude millimeter-wave modulated modulation modulation;error monolithic multigigabit networks;error networks;submillimetre noise;Wireless noise;extremely noise;nonideal noise;quadrature oscillator phase phase-shift range;symbol rate rate;Estimation;Modulation;Phase rates;wireless shift signals;relative statistics;millimetre submillimeter-wave systems;Bandwidth;Bit vector waves;phase waves;wireless wireless","misc":{"bdsk-url-1":"https://doi.org/10.1109/TMTT.2015.2467390","doi":"10.1109/TMTT.2015.2467390"},"note":"","number":"10","number-of-pages":"11","page":"3288--3299","page-first":"3288","publisher":"","publisher-place":"","status":"","title":"Performance Estimation for Broadband Multi-Gigabit Millimeter and Sub-Millimeter Wave Wireless Communication Links","type":"article-journal","username":"ingmarkallfass","version":"","volume":"63"},"f698e236a380faddfb8f96d98b28f5bcinue":{"DOI":"10.1109/JSTSP.2017.2784180","ISBN":"","ISSN":"1941-0484","URL":"","abstract":"","annote":"","author":[{"family":"Dörner","given":"S."},{"family":"Cammerer","given":"S."},{"family":"Hoydis","given":"J."},{"family":"ten Brink","given":"S."}],"citation-label":"learning_to_communicate","collection-editor":[],"collection-title":"","container-author":[],"container-title":"IEEE Journal of Selected Topics in Signal Processing","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2018","Feb"]],"literal":"2018"},"event-place":"","id":"f698e236a380faddfb8f96d98b28f5bcinue","interhash":"a0e38e6df23c2f25303e9abd1d9fd60d","intrahash":"f698e236a380faddfb8f96d98b28f5bc","issue":"1","issued":{"date-parts":[["2018","Feb"]],"literal":"2018"},"keyword":"myown network;over-the-air;software-defined software-defined from:sdnr transmissions;open-source (artificial systems;block-based module;transmitter transmission;receiver implementations;deep computing;two-step nets;radio intelligence);neural libraries;continuous learning;communications learning;end-to-end rate;over-the-air synchronization;frame error transmissions;receiver deep neural software synchronization data learning;modulation;neural learning libraries;software radio implementations;off-the-shelf networks;NNs;block procedure;end-to-end radio;synchronisation;telecommunication radios;Training;Receivers;Communication networks;Hardware;Transmitters;Synchronization;Autoencoder;communication;deep receivers;software systems;Artificial","misc":{"issn":"1941-0484","doi":"10.1109/JSTSP.2017.2784180"},"note":"","number":"1","number-of-pages":"11","page":"132-143","page-first":"132","publisher":"","publisher-place":"","status":"","title":"Deep Learning Based Communication Over the Air","type":"article-journal","username":"inue","version":"","volume":"12"},"ee7ff3227f584612ccaf760df2e7d567annettegugel":{"DOI":"","ISBN":"","ISSN":"","URL":"https://www.ieh.uni-stuttgart.de/dokumente/publikationen/2019_09_Gross_Evaluation_of_a_Three-Phase_Distribution_System_State.pdf","abstract":"","annote":"","author":[{"family":"Groß","given":"Daniel"},{"family":"Früh","given":"Heiner"},{"family":"Contreras","given":"Daniel"},{"family":"Rudion","given":"Krzysztof"},{"family":"Rupp","given":"Linda"},{"family":"Lakenbrink","given":"Christian"}],"citation-label":"gross2019evaluation","collection-editor":[],"collection-title":"","container-author":[],"container-title":"","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2019","09"]],"literal":"2019"},"event-place":"","id":"ee7ff3227f584612ccaf760df2e7d567annettegugel","interhash":"458fd6ed132c0be9d143af324cb67abe","intrahash":"ee7ff3227f584612ccaf760df2e7d567","issue":"","issued":{"date-parts":[["2019","09"]],"literal":"2019"},"keyword":"data distribution error estimation measurement measurements medium meter placement pseudo real state system three-phase voltage","misc":{"eventtitle":"2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe)","venue":"Bucharest, Romania","eventdate":"September"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"Evaluation of a Three-Phase Distribution System State Estimation for Operational Use in a Real Medium Voltage Grid","type":"paper-conference","username":"annettegugel","version":"","volume":""},"699c9caf6155e0598d9c980105b8118dmathematik":{"DOI":"10.1016/j.sysconle.2011.10.012","ISBN":"","ISSN":"","URL":"http://www.sciencedirect.com/science/article/pii/S0167691111002672","abstract":"In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.","annote":"","author":[{"family":"Wirtz","given":"D."},{"family":"Haasdonk","given":"B."}],"citation-label":"wirtz2012efficient","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Systems and Control Letters","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"699c9caf6155e0598d9c980105b8118dmathematik","interhash":"e80ae72fe2c1f9f79f4f7f8f5ce00735","intrahash":"699c9caf6155e0598d9c980105b8118d","issue":"1","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori decomposition, dynamical error estimates, from:mhartmann ians kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig","misc":{"file":":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF","doi":"10.1016/j.sysconle.2011.10.012"},"note":"","number":"1","number-of-pages":"8","page":"203 - 211","page-first":"203","publisher":"","publisher-place":"","status":"","title":"Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems","type":"article-journal","username":"mathematik","version":"","volume":"61"},"a795baaf1eb095e7f7ab84a05f884ad8mathematik":{"DOI":"10.1002/num.22065","ISBN":"","ISSN":"1098-2426","URL":"http://dx.doi.org/10.1002/num.22065","abstract":"","annote":"","author":[{"family":"Gaspoz","given":"F. D."},{"family":"Morin","given":"P."},{"family":"Veeser","given":"A."}],"citation-label":"gaspoz2017posteriori","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Numerical Methods for Partial Differential Equations","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2017"]],"literal":"2017"},"event-place":"","id":"a795baaf1eb095e7f7ab84a05f884ad8mathematik","interhash":"fea501ed2a4ad0de2f63886c01491c60","intrahash":"a795baaf1eb095e7f7ab84a05f884ad8","issue":"4","issued":{"date-parts":[["2017"]],"literal":"2017"},"keyword":"Dirac Sobolev a adaptivity, element error estimators, finite fractional from:mhartmann ians mass, methods, posteriori spaces vorlaeufig","misc":{"issn":"1098-2426","owner":"langeras","doi":"10.1002/num.22065"},"note":"","number":"4","number-of-pages":"24","page":"1018--1042","page-first":"1018","publisher":"","publisher-place":"","status":"","title":"A posteriori error estimates with point sources in fractional sobolev\n\tspaces","type":"article-journal","username":"mathematik","version":"","volume":"33"},"4276d5a0313937597a16f8ab9f50ce70mathematik":{"DOI":"","ISBN":"","ISSN":"","URL":"https://arxiv.org/abs/1610.06814","abstract":"","annote":"","author":[{"family":"Gaspoz","given":"F. 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For A being a variable coefficient matrix with possible\n\tjump discontinuities, we provide a complete a posteriori error analysis\n\twhich applies to both Raviart�Thomas R","annote":"","author":[{"family":"Cascón","given":"J. Manuel"},{"family":"Nochetto","given":"Ricardo H."},{"family":"Siebert","given":"Kunibert G."}],"citation-label":"cascon2007design","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Mathematical Models & Methods in Applied Sciences","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2007"]],"literal":"2007"},"event-place":"","id":"f5f80e984a2acb11eefec6e697309130mathematik","interhash":"0455c6fff7212a7c27b39d27400fc025","intrahash":"f5f80e984a2acb11eefec6e697309130","issue":"11","issued":{"date-parts":[["2007"]],"literal":"2007"},"keyword":"A convergence; error estimate; from:mhartmann ians multigrid oscillation; posteriori preconditioning reduction; vorlaeufig","misc":{"owner":"kohlsk","doi":"10.1142/S0218202507002492"},"note":"","number":"11","number-of-pages":"32","page":"1849--1881","page-first":"1849","publisher":"","publisher-place":"","status":"","title":"Design and Convergence of AFEM in $H(div)$","type":"article-journal","username":"mathematik","version":"","volume":"17"},"c9ff784e6a0440b80b45055fa2c9df7emathematik":{"DOI":"","ISBN":"","ISSN":"","URL":"http://www.ifac-papersonline.net/","abstract":"This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"wirtz2012aposteriori","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"c9ff784e6a0440b80b45055fa2c9df7emathematik","interhash":"e6dce191069323c30bda8a87cce2913a","intrahash":"c9ff784e6a0440b80b45055fa2c9df7e","issue":"","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori decomposition, dynamical error estimates, from:mhartmann ians kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig","misc":{"owner":"haasdonk"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A-posteriori error estimation for parameterized kernel-based systems","type":"paper-conference","username":"mathematik","version":"","volume":""},"992b581f1e96812159406b320cdc362cmathematik":{"DOI":"","ISBN":"","ISSN":"","URL":"","abstract":"","annote":"","author":[{"family":"Gaspoz","given":"Fernando D."},{"family":"Morin","given":"Pedro"}],"citation-label":"gaspoz2009convergence","collection-editor":[],"collection-title":"","container-author":[],"container-title":"IMA J. 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Anal.","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2009"]],"literal":"2009"},"event-place":"","id":"992b581f1e96812159406b320cdc362cmathematik","interhash":"1e7a0334d6389891fae356da35076ece","intrahash":"992b581f1e96812159406b320cdc362c","issue":"4","issued":{"date-parts":[["2009"]],"literal":"2009"},"keyword":"a adaptive elliptic equations error estimator, from:mhartmann ians mesh posteriori refinement, vorlaeufig","misc":{"owner":"szur","fjournal":"IMA Journal on Numerical Analysis"},"note":"","number":"4","number-of-pages":"19","page":"917--936","page-first":"917","publisher":"Oxford University Press","publisher-place":"","status":"","title":"Convergence rates for adaptive finite elements","type":"article-journal","username":"mathematik","version":"","volume":"29"},"a795baaf1eb095e7f7ab84a05f884ad8mhartmann":{"DOI":"10.1002/num.22065","ISBN":"","ISSN":"1098-2426","URL":"http://dx.doi.org/10.1002/num.22065","abstract":"","annote":"","author":[{"family":"Gaspoz","given":"F. D."},{"family":"Morin","given":"P."},{"family":"Veeser","given":"A."}],"citation-label":"gaspoz2017posteriori","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Numerical Methods for Partial Differential Equations","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2017"]],"literal":"2017"},"event-place":"","id":"a795baaf1eb095e7f7ab84a05f884ad8mhartmann","interhash":"fea501ed2a4ad0de2f63886c01491c60","intrahash":"a795baaf1eb095e7f7ab84a05f884ad8","issue":"4","issued":{"date-parts":[["2017"]],"literal":"2017"},"keyword":"Dirac Sobolev a adaptivity, element error estimators, finite fractional mass, methods, posteriori spaces vorlaeufig","misc":{"issn":"1098-2426","owner":"langeras","doi":"10.1002/num.22065"},"note":"","number":"4","number-of-pages":"24","page":"1018--1042","page-first":"1018","publisher":"","publisher-place":"","status":"","title":"A posteriori error estimates with point sources in fractional sobolev\n\tspaces","type":"article-journal","username":"mhartmann","version":"","volume":"33"},"699c9caf6155e0598d9c980105b8118dmhartmann":{"DOI":"10.1016/j.sysconle.2011.10.012","ISBN":"","ISSN":"","URL":"http://www.sciencedirect.com/science/article/pii/S0167691111002672","abstract":"In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.","annote":"","author":[{"family":"Wirtz","given":"D."},{"family":"Haasdonk","given":"B."}],"citation-label":"wirtz2012efficient","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Systems and Control Letters","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"699c9caf6155e0598d9c980105b8118dmhartmann","interhash":"e80ae72fe2c1f9f79f4f7f8f5ce00735","intrahash":"699c9caf6155e0598d9c980105b8118d","issue":"1","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig","misc":{"file":":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF","doi":"10.1016/j.sysconle.2011.10.012"},"note":"","number":"1","number-of-pages":"8","page":"203 - 211","page-first":"203","publisher":"","publisher-place":"","status":"","title":"Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems","type":"article-journal","username":"mhartmann","version":"","volume":"61"},"4276d5a0313937597a16f8ab9f50ce70mhartmann":{"DOI":"","ISBN":"","ISSN":"","URL":"https://arxiv.org/abs/1610.06814","abstract":"","annote":"","author":[{"family":"Gaspoz","given":"F. 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