{"992b581f1e96812159406b320cdc362cmhartmann":{"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. Numer. Anal.","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2009"]],"literal":"2009"},"event-place":"","id":"992b581f1e96812159406b320cdc362cmhartmann","interhash":"1e7a0334d6389891fae356da35076ece","intrahash":"992b581f1e96812159406b320cdc362c","issue":"4","issued":{"date-parts":[["2009"]],"literal":"2009"},"keyword":"a estimator, equations posteriori adaptive error refinement, vorlaeufig elliptic mesh","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":"mhartmann","version":"","volume":"29"},"c9ff784e6a0440b80b45055fa2c9df7emhartmann":{"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":"c9ff784e6a0440b80b45055fa2c9df7emhartmann","interhash":"e6dce191069323c30bda8a87cce2913a","intrahash":"c9ff784e6a0440b80b45055fa2c9df7e","issue":"","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, parameterized projection estimates, model vorlaeufig reduction,","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":"mhartmann","version":"","volume":""},"f5f80e984a2acb11eefec6e697309130mhartmann":{"DOI":"10.1142/S0218202507002492","ISBN":"","ISSN":"","URL":"http://dx.doi.org/10.1142/S0218202507002492","abstract":"We design an adaptive finite element method (AFEM) for mixed boundary\n\tvalue problems associated with the differential operator A-?div in\n\tH(div, O). 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":"f5f80e984a2acb11eefec6e697309130mhartmann","interhash":"0455c6fff7212a7c27b39d27400fc025","intrahash":"f5f80e984a2acb11eefec6e697309130","issue":"11","issued":{"date-parts":[["2007"]],"literal":"2007"},"keyword":"A convergence; posteriori reduction; error estimate; multigrid oscillation; preconditioning 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":"mhartmann","version":"","volume":"17"},"cc6b799a8d34f87ec3cd593a8053b3aemhartmann":{"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":"B."}],"citation-label":"martini2015reduced","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":"cc6b799a8d34f87ec3cd593a8053b3aemhartmann","interhash":"1474e2e0db6128c1ec02771a5ff8841b","intrahash":"cc6b799a8d34f87ec3cd593a8053b3ae","issue":"5","issued":{"date-parts":[["2015"]],"literal":"2015"},"keyword":"Error decomposition; medium 76D07 Porous Reduced method; basis problem; Stokes estimation; 76S05; equation; Non-coercive Domain flow; vorlaeufig 65N55;","misc":{"file":":http\\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Maier2014a_www_RB_stokes_darcy_preprint.pdf:PDF","owner":"maieril","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\n\tthe coupled Stokes-Darcy system","type":"article-journal","username":"mhartmann","version":"","volume":"41"},"4276d5a0313937597a16f8ab9f50ce70mhartmann":{"DOI":"","ISBN":"","ISSN":"","URL":"https://arxiv.org/abs/1610.06814","abstract":"","annote":"","author":[{"family":"Gaspoz","given":"F. D."},{"family":"Kreuzer","given":"C."},{"family":"Siebert","given":"K."},{"family":"Ziegler","given":"D."}],"citation-label":"gaspoz2017convergent","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Submitted","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2017"]],"literal":"2017"},"event-place":"","id":"4276d5a0313937597a16f8ab9f50ce70mhartmann","interhash":"590acae3fb93ecdb48f22ba922444179","intrahash":"4276d5a0313937597a16f8ab9f50ce70","issue":"","issued":{"date-parts":[["2017"]],"literal":"2017"},"keyword":"a equation estimators, convergence, error finite methods, posteriori adaptivity, element vorlaeufig heat","misc":{"owner":"langeras"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A convergent time-space adaptive $dG(s)$ finite element method for\n\tparabolic problems motivated by equal error distribution","type":"manuscript","username":"mhartmann","version":"","volume":""},"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":"a Dirac estimators, error finite fractional methods, posteriori adaptivity, element spaces mass, Sobolev 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":"subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, projection estimates, model vorlaeufig reduction,","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"}}