{ "types" : { "Bookmark" : { "pluralLabel" : "Bookmarks" }, "Publication" : { "pluralLabel" : "Publications" }, "GoldStandardPublication" : { "pluralLabel" : "GoldStandardPublications" }, "GoldStandardBookmark" : { "pluralLabel" : "GoldStandardBookmarks" }, "Tag" : { "pluralLabel" : "Tags" }, "User" : { "pluralLabel" : "Users" }, "Group" : { "pluralLabel" : "Groups" }, "Sphere" : { "pluralLabel" : "Spheres" } }, "properties" : { "count" : { "valueType" : "number" }, "date" : { "valueType" : "date" }, "changeDate" : { "valueType" : "date" }, "url" : { "valueType" : "url" }, "id" : { "valueType" : "url" }, "tags" : { "valueType" : "item" }, "user" : { "valueType" : "item" } }, "items" : [ { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2992b581f1e96812159406b320cdc362c/mhartmann", "tags" : [ "a","estimator,","equations","posteriori","adaptive","error","refinement,","vorlaeufig","elliptic","mesh" ], "intraHash" : "992b581f1e96812159406b320cdc362c", "interHash" : "1e7a0334d6389891fae356da35076ece", "label" : "Convergence rates for adaptive finite elements", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 5, "pub-type": "article", "journal": "IMA J. Numer. Anal.","publisher":"Oxford University Press", "year": "2009", "url": "", "author": [ "Fernando D. Gaspoz","Pedro Morin" ], "authors": [ {"first" : "Fernando D.", "last" : "Gaspoz"}, {"first" : "Pedro", "last" : "Morin"} ], "volume": "29","number": "4","pages": "917--936", "owner" : "szur", "fjournal" : "IMA Journal on Numerical Analysis", "bibtexKey": "gaspoz2009convergence" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmann", "tags" : [ "subspace","error","dynamical","kernel","a-posteriori","methods,","systems,","nonlinear","offline/online","decomposition,","parameterized","projection","estimates,","model","vorlaeufig","reduction," ], "intraHash" : "c9ff784e6a0440b80b45055fa2c9df7e", "interHash" : "e6dce191069323c30bda8a87cce2913a", "label" : "A-posteriori error estimation for parameterized kernel-based systems", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 8, "pub-type": "inproceedings", "booktitle": "Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling", "year": "2012", "url": "http://www.ifac-papersonline.net/", "author": [ "Daniel Wirtz","Bernard Haasdonk" ], "authors": [ {"first" : "Daniel", "last" : "Wirtz"}, {"first" : "Bernard", "last" : "Haasdonk"} ], "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.", "owner" : "haasdonk", "bibtexKey": "wirtz2012aposteriori" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2f5f80e984a2acb11eefec6e697309130/mhartmann", "tags" : [ "A","convergence;","posteriori","reduction;","error","estimate;","multigrid","oscillation;","preconditioning","vorlaeufig" ], "intraHash" : "f5f80e984a2acb11eefec6e697309130", "interHash" : "0455c6fff7212a7c27b39d27400fc025", "label" : "Design and Convergence of AFEM in $H(div)$", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 2, "pub-type": "article", "journal": "Mathematical Models & Methods in Applied Sciences", "year": "2007", "url": "http://dx.doi.org/10.1142/S0218202507002492", "author": [ "J. Manuel Cascón","Ricardo H. Nochetto","Kunibert G. Siebert" ], "authors": [ {"first" : "J. Manuel", "last" : "Cascón"}, {"first" : "Ricardo H.", "last" : "Nochetto"}, {"first" : "Kunibert G.", "last" : "Siebert"} ], "volume": "17","number": "11","pages": "1849--1881","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", "owner" : "kohlsk", "doi" : "10.1142/S0218202507002492", "bibtexKey": "cascon2007design" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2cc6b799a8d34f87ec3cd593a8053b3ae/mhartmann", "tags" : [ "Error","decomposition;","medium","76D07","Porous","Reduced","method;","basis","problem;","Stokes","estimation;","76S05;","equation;","Non-coercive","Domain","flow;","vorlaeufig","65N55;" ], "intraHash" : "cc6b799a8d34f87ec3cd593a8053b3ae", "interHash" : "1474e2e0db6128c1ec02771a5ff8841b", "label" : "Reduced basis approximation and a-posteriori error estimation for\n\tthe coupled Stokes-Darcy system", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 12, "pub-type": "article", "journal": "Advances in Computational Mathematics", "year": "2015", "url": "http://link.springer.com/article/10.1007/s10444-014-9396-6", "author": [ "I. Martini","G. Rozza","B. Haasdonk" ], "authors": [ {"first" : "I.", "last" : "Martini"}, {"first" : "G.", "last" : "Rozza"}, {"first" : "B.", "last" : "Haasdonk"} ], "volume": "41","number": "5","pages": "1131--1157", "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", "bibtexKey": "martini2015reduced" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/24276d5a0313937597a16f8ab9f50ce70/mhartmann", "tags" : [ "a","equation","estimators,","convergence,","error","finite","methods,","posteriori","adaptivity,","element","vorlaeufig","heat" ], "intraHash" : "4276d5a0313937597a16f8ab9f50ce70", "interHash" : "590acae3fb93ecdb48f22ba922444179", "label" : "A convergent time-space adaptive $dG(s)$ finite element method for\n\tparabolic problems motivated by equal error distribution", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 2, "pub-type": "unpublished", "journal": "Submitted", "year": "2017", "url": "https://arxiv.org/abs/1610.06814", "author": [ "F. D. Gaspoz","C. Kreuzer","K. Siebert","D. Ziegler" ], "authors": [ {"first" : "F. D.", "last" : "Gaspoz"}, {"first" : "C.", "last" : "Kreuzer"}, {"first" : "K.", "last" : "Siebert"}, {"first" : "D.", "last" : "Ziegler"} ], "owner" : "langeras", "bibtexKey": "gaspoz2017convergent" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2a795baaf1eb095e7f7ab84a05f884ad8/mhartmann", "tags" : [ "a","Dirac","estimators,","error","finite","fractional","methods,","posteriori","adaptivity,","element","spaces","mass,","Sobolev","vorlaeufig" ], "intraHash" : "a795baaf1eb095e7f7ab84a05f884ad8", "interHash" : "fea501ed2a4ad0de2f63886c01491c60", "label" : "A posteriori error estimates with point sources in fractional sobolev\n\tspaces", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 7, "pub-type": "article", "journal": "Numerical Methods for Partial Differential Equations", "year": "2017", "url": "http://dx.doi.org/10.1002/num.22065", "author": [ "F. D. Gaspoz","P. Morin","A. Veeser" ], "authors": [ {"first" : "F. D.", "last" : "Gaspoz"}, {"first" : "P.", "last" : "Morin"}, {"first" : "A.", "last" : "Veeser"} ], "volume": "33","number": "4","pages": "1018--1042", "issn" : "1098-2426", "owner" : "langeras", "doi" : "10.1002/num.22065", "bibtexKey": "gaspoz2017posteriori" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmann", "tags" : [ "subspace","error","dynamical","kernel","a-posteriori","methods,","systems,","nonlinear","offline/online","decomposition,","projection","estimates,","model","vorlaeufig","reduction," ], "intraHash" : "699c9caf6155e0598d9c980105b8118d", "interHash" : "e80ae72fe2c1f9f79f4f7f8f5ce00735", "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 11, "pub-type": "article", "journal": "Systems and Control Letters", "year": "2012", "url": "http://www.sciencedirect.com/science/article/pii/S0167691111002672", "author": [ "D. Wirtz","B. Haasdonk" ], "authors": [ {"first" : "D.", "last" : "Wirtz"}, {"first" : "B.", "last" : "Haasdonk"} ], "volume": "61","number": "1","pages": "203 - 211","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.", "file" : ":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF", "doi" : "10.1016/j.sysconle.2011.10.012", "bibtexKey": "wirtz2012efficient" } ] }