Edit Profile (opens in new tab) Eigel, Martin Co-Author Distance Author ID: eigel.martin Published as: Eigel, Martin; Eigel, M. External Links: MGP Documents Indexed: 43 Publications since 2005, including 8 Additional arXiv Preprints Co-Authors: 78 Co-Authors with 43 Joint Publications 1,698 Co-Co-Authors all top 5 Co-Authors 0 single-authored 8 Schneider, Reinhold 7 Gruhlke, Robert 6 Trunschke, Philipp 5 Neumann, Johannes 4 Marschall, Manuel 3 Bayer, Christian 3 Carstensen, Carsten 3 George, Erwin 3 Grasedyck, Lars 3 Kirkilionis, Markus A. 3 Merdon, Christian 3 Moser, Dieter 3 Sommer, David 3 Wolf, Sebastian 2 Anker, Felix 2 Drieschner, Martin 2 Ehre, Max 2 Farchmin, Nando 2 Gittelson, Claude Jeffrey 2 Heidenreich, Sebastian 2 Hömberg, Dietmar 2 Miranda, Charles 2 Papaioannou, Iason 2 Petryna, Yuri 2 Pfeffer, Max 2 Schoenmakers, John G. M. 2 Schwab, Christoph 2 Straub, Daniel 2 Zander, Elmar K. 1 Athale, Chaitanya A. 1 Bastian, Peter 1 Biehler, Jonas 1 Brumme, Stephan 1 Daub, Marco 1 Domijan, Mirela 1 Duddeck, Fabian M. E. 1 Eichner, Lukas 1 Eils, Roland 1 Ernst, Oliver G. 1 Gedicke, Joscha 1 Götz, Marco 1 Graf, Wolfgang 1 Gühring, Ingo 1 Hegemann, Nando 1 Heiss, Cosmas 1 Henning, Carla 1 Hermann, Harald 1 Hoppe, Ronald H. W. 1 Kaliske, Michael 1 Kappel, Constantin 1 Kastian, Steffen 1 Kohlsche, Thomas 1 Ladkau, Marcel 1 Leyendecker, Sigrid 1 Li, Mike 1 Löbhard, Caroline 1 Müller, Rüdiger 1 Multerer, Michael D. 1 Nouy, Anthony 1 Ostermeyer, Georg-Peter 1 Peterseim, Daniel 1 Pfaller, Martin R. 1 Pivovarov, Dmytro 1 Reese, Stefanie 1 Ricken, Tim 1 Sallandt, Leon 1 Samrowski, Tatiana S. 1 Sbano, Luca 1 Schütte, Janina 1 Sprungk, Björn 1 Srisupattarawanit, Tarin 1 Steinmann, Paul 1 Sturm, Kevin 1 Tamellini, Lorenzo 1 Volz, Dietmar 1 von Estorff, Otto 1 Wall, Wolfgang A. 1 Willner, Kai all top 5 Serials 4 Computer Methods in Applied Mechanics and Engineering 4 Computational Methods in Applied Mathematics 3 SIAM/ASA Journal on Uncertainty Quantification 2 IMA Journal of Numerical Analysis 2 Numerische Mathematik 2 SIAM Journal on Scientific Computing 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 GAMM-Mitteilungen 1 Inverse Problems 1 SIAM Journal on Numerical Analysis 1 Computational Mechanics 1 Journal of Scientific Computing 1 Numerical Linear Algebra with Applications 1 Advances in Computational Mathematics 1 Optimization Methods & Software 1 Numerical Mathematics: Theory, Methods and Applications 1 SIAM Journal on Financial Mathematics 1 Statistics and Computing 1 International Journal for Uncertainty Quantification all top 5 Fields 31 Numerical analysis (65-XX) 21 Partial differential equations (35-XX) 15 Probability theory and stochastic processes (60-XX) 7 Operator theory (47-XX) 7 Statistics (62-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Computer science (68-XX) 5 Mechanics of deformable solids (74-XX) 3 Biology and other natural sciences (92-XX) 3 Systems theory; control (93-XX) 2 Approximations and expansions (41-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Functional analysis (46-XX) 1 Fluid mechanics (76-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 23 Publications have been cited 293 times in 187 Documents Cited by ▼ Year ▼ Adaptive stochastic Galerkin FEM. Zbl 1296.65157 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 65 2014 A review of unified a posteriori finite element error control. Zbl 1289.65249 Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 32 2012 A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes. Zbl 1335.65006 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 30 2015 Adaptive stochastic Galerkin FEM with hierarchical tensor representations. Zbl 1397.65262 Eigel, Martin; Pfeffer, Max; Schneider, Reinhold 27 2017 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172 Carstensen, C.; Eigel, M.; Gedicke, J. 21 2011 An adaptive multilevel Monte Carlo method with stochastic bounds for quantities of interest with uncertain data. Zbl 1398.35306 Eigel, Martin; Merdon, Christian; Neumann, Johannes 19 2016 Local equilibration error estimators for guaranteed error control in adaptive stochastic higher-order Galerkin finite element methods. Zbl 1398.65297 Eigel, Martin; Merdon, Christian 17 2016 Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization. Zbl 1388.35036 Eigel, M.; Sturm, Kevin 13 2018 Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations. Zbl 1439.65160 Eigel, Martin; Marschall, Manuel; Pfeffer, Max; Schneider, Reinhold 10 2020 Sampling-free Bayesian inversion with adaptive hierarchical tensor representations. Zbl 1404.65261 Eigel, Martin; Marschall, Manuel; Schneider, Reinhold 9 2018 Variational Monte Carlo – bridging concepts of machine learning and high-dimensional partial differential equations. Zbl 1435.68258 Eigel, Martin; Schneider, Reinhold; Trunschke, Philipp; Wolf, Sebastian 9 2019 Non-intrusive tensor reconstruction for high-dimensional random PDEs. Zbl 1419.35259 Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian 7 2019 SDE based regression for linear random PDEs. Zbl 1372.65012 Anker, Felix; Bayer, Christian; Eigel, Martin; Ladkau, Marcel; Neumann, Johannes; Schoenmakers, John 5 2017 On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion. Zbl 1508.65163 Eigel, Martin; Ernst, Oliver G.; Sprungk, Björn; Tamellini, Lorenzo 5 2022 Equilibration a posteriori error estimation for convection-diffusion-reaction problems. Zbl 1353.65113 Eigel, M.; Merdon, C. 4 2016 Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion. Zbl 1484.62002 Eigel, Martin; Gruhlke, Robert; Marschall, Manuel 4 2022 A mesh-free partition of unity method for diffusion equations on complex domains. Zbl 1195.65169 Eigel, M.; George, E.; Kirkilionis, M. 3 2010 An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains. Zbl 1447.65137 Eigel, Martin; Marschall, Manuel; Multerer, Michael 3 2020 The partition of unity meshfree method for solving transport-reaction equations on complex domains: implementation and applications in the life sciences. Zbl 1156.92012 Eigel, Martin; George, Erwin; Kirkilianis, Markus 2 2008 Simulation of composite materials by a network FEM with error control. Zbl 1309.74069 Eigel, Martin; Peterseim, Daniel 2 2015 Risk averse stochastic structural topology optimization. Zbl 1440.74291 Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian 2 2018 Convergence bounds for empirical nonlinear least-squares. Zbl 1482.62071 Eigel, Martin; Schneider, Reinhold; Trunschke, Philipp 2 2022 Functional a posteriori error estimation for stationary reaction-convection-diffusion problems. Zbl 1284.65167 Eigel, Martin; Samrowski, Tatiana 2 2014 On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion. Zbl 1508.65163 Eigel, Martin; Ernst, Oliver G.; Sprungk, Björn; Tamellini, Lorenzo 5 2022 Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion. Zbl 1484.62002 Eigel, Martin; Gruhlke, Robert; Marschall, Manuel 4 2022 Convergence bounds for empirical nonlinear least-squares. Zbl 1482.62071 Eigel, Martin; Schneider, Reinhold; Trunschke, Philipp 2 2022 Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations. Zbl 1439.65160 Eigel, Martin; Marschall, Manuel; Pfeffer, Max; Schneider, Reinhold 10 2020 An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains. Zbl 1447.65137 Eigel, Martin; Marschall, Manuel; Multerer, Michael 3 2020 Variational Monte Carlo – bridging concepts of machine learning and high-dimensional partial differential equations. Zbl 1435.68258 Eigel, Martin; Schneider, Reinhold; Trunschke, Philipp; Wolf, Sebastian 9 2019 Non-intrusive tensor reconstruction for high-dimensional random PDEs. Zbl 1419.35259 Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian 7 2019 Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization. Zbl 1388.35036 Eigel, M.; Sturm, Kevin 13 2018 Sampling-free Bayesian inversion with adaptive hierarchical tensor representations. Zbl 1404.65261 Eigel, Martin; Marschall, Manuel; Schneider, Reinhold 9 2018 Risk averse stochastic structural topology optimization. Zbl 1440.74291 Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian 2 2018 Adaptive stochastic Galerkin FEM with hierarchical tensor representations. Zbl 1397.65262 Eigel, Martin; Pfeffer, Max; Schneider, Reinhold 27 2017 SDE based regression for linear random PDEs. Zbl 1372.65012 Anker, Felix; Bayer, Christian; Eigel, Martin; Ladkau, Marcel; Neumann, Johannes; Schoenmakers, John 5 2017 An adaptive multilevel Monte Carlo method with stochastic bounds for quantities of interest with uncertain data. Zbl 1398.35306 Eigel, Martin; Merdon, Christian; Neumann, Johannes 19 2016 Local equilibration error estimators for guaranteed error control in adaptive stochastic higher-order Galerkin finite element methods. Zbl 1398.65297 Eigel, Martin; Merdon, Christian 17 2016 Equilibration a posteriori error estimation for convection-diffusion-reaction problems. Zbl 1353.65113 Eigel, M.; Merdon, C. 4 2016 A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes. Zbl 1335.65006 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 30 2015 Simulation of composite materials by a network FEM with error control. Zbl 1309.74069 Eigel, Martin; Peterseim, Daniel 2 2015 Adaptive stochastic Galerkin FEM. Zbl 1296.65157 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 65 2014 Functional a posteriori error estimation for stationary reaction-convection-diffusion problems. Zbl 1284.65167 Eigel, Martin; Samrowski, Tatiana 2 2014 A review of unified a posteriori finite element error control. Zbl 1289.65249 Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 32 2012 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172 Carstensen, C.; Eigel, M.; Gedicke, J. 21 2011 A mesh-free partition of unity method for diffusion equations on complex domains. Zbl 1195.65169 Eigel, M.; George, E.; Kirkilionis, M. 3 2010 The partition of unity meshfree method for solving transport-reaction equations on complex domains: implementation and applications in the life sciences. Zbl 1156.92012 Eigel, Martin; George, Erwin; Kirkilianis, Markus 2 2008 all cited Publications top 5 cited Publications all top 5 Cited by 311 Authors 20 Carstensen, Carsten 18 Eigel, Martin 12 Bespalov, Alexei 11 Schneider, Reinhold 10 Silvester, David J. 9 Powell, Catherine Elizabeth 8 Dolgov, Sergey V. 7 Merdon, Christian 7 Schwab, Christoph 6 Hu, Jun 6 Scheichl, Robert 5 Bachmayr, Markus 5 Nobile, Fabio 4 Bayer, Christian 4 Marschall, Manuel 4 Nataraj, Neela 4 Neumann, Johannes 4 Praetorius, Dirk 4 Rocchi, Leonardo 4 Trunschke, Philipp 4 Zhang, Shangyou 3 Feischl, Michael 3 Gedicke, Joscha 3 Gerster, Stephan 3 Khan, Arbaz 3 Khoromskiĭ, Boris Nikolaevich 3 Li, Minghao 3 Man, Hongying 3 Pfeffer, Max 3 Pinnau, René 3 Pultarová, Ivana 3 Ruggeri, Michele 3 Sallandt, Leon 3 Schoenmakers, John G. M. 3 Shi, Dongyang 3 Sturm, Kevin 3 Vohralík, Martin 2 Aquino, Wilkins 2 Bacuta, Constantin 2 Bertrand, Fleurianne 2 Bordas, Stéphane Pierre Alain 2 Bringmann, Philipp 2 Bungartz, Hans-Joachim 2 Crowder, Adam J. 2 Cui, Tiangang 2 Dai, Dihan 2 De Gersem, Herbert 2 Dietrich, Nicolas 2 Dond, Asha K. 2 Ebeling-Rump, Moritz 2 Epshteyn, Yekaterina 2 Farcas, Ionut-Gabriel 2 Gallistl, Dietmar 2 Gittelson, Claude Jeffrey 2 Grasedyck, Lars 2 Guignard, Diane 2 Hellwig, Friederike 2 Herty, Michael Matthias 2 Hömberg, Dietmar 2 Jacavage, Jacob 2 Kämmerer, Lutz 2 Kouri, Drew P. 2 Kressner, Daniel 2 Kutyniok, Gitta 2 Lasarzik, Robert 2 Laurain, Antoine 2 Li, Jichun 2 Loukrezis, Dimitrios 2 Marx, Thomas 2 Matthies, Hermann Georg 2 Multerer, Michael D. 2 Narayan, Akil C. 2 Neckel, Tobias 2 Oster, Mathias 2 Peherstorfer, Benjamin 2 Petersen, Philipp Christian 2 Potts, Daniel 2 Raslan, Mones 2 Redmann, Martin 2 Scarabosio, Laura 2 Tamellini, Lorenzo 2 Tempone, Raúl F. 2 Tran, Ngoc Tien 2 Uschmajew, André 2 Wolf, Sebastian 2 Xu, Feng 2 Zander, Elmar K. 2 Zou, Zilong 1 Agud, Lucía 1 Ainsworth, Mark 1 Allaire, Doug 1 Anaya-Izquierdo, Karim Alejandro 1 Anker, Felix 1 Aznaran, Francis R. A. 1 Ballani, Jonas 1 Barth, Andrea 1 Bean, Maranda 1 Beck, Andrea D. 1 Beck, Christian 1 Beck, Joakim ...and 211 more Authors all top 5 Cited in 58 Serials 19 SIAM Journal on Scientific Computing 17 Computer Methods in Applied Mechanics and Engineering 17 SIAM/ASA Journal on Uncertainty Quantification 11 SIAM Journal on Numerical Analysis 10 Numerische Mathematik 8 Computers & Mathematics with Applications 8 Journal of Scientific Computing 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Journal of Computational Physics 4 Mathematics of Computation 4 Numerical Methods for Partial Differential Equations 4 Computational Methods in Applied Mathematics 3 Applied Mathematics and Computation 3 Journal of Computational and Applied Mathematics 3 Advances in Computational Mathematics 2 Inverse Problems 2 Calcolo 2 International Journal for Numerical Methods in Engineering 2 Computational and Applied Mathematics 2 Journal of Numerical Mathematics 2 Science China. Mathematics 2 Statistics and Computing 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Journal of Mathematical Analysis and Applications 1 BIT 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Control and Optimization 1 Constructive Approximation 1 Applications of Mathematics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 SIAM Journal on Optimization 1 Applied and Computational Harmonic Analysis 1 Engineering Analysis with Boundary Elements 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Quantitative Finance 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Multiscale Modeling & Simulation 1 Analysis and Applications (Singapore) 1 Acta Numerica 1 Communications in Computational Physics 1 SIAM Journal on Financial Mathematics 1 International Journal of Advances in Engineering Sciences and Applied Mathematics 1 Journal of Mathematics in Industry 1 Communications in Mathematics and Statistics 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 SMAI Journal of Computational Mathematics 1 SN Partial Differential Equations and Applications 1 Sampling Theory, Signal Processing, and Data Analysis 1 Journal of Computational Physics: X all top 5 Cited in 32 Fields 167 Numerical analysis (65-XX) 89 Partial differential equations (35-XX) 43 Probability theory and stochastic processes (60-XX) 31 Mechanics of deformable solids (74-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 16 Fluid mechanics (76-XX) 15 Statistics (62-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 9 Operator theory (47-XX) 9 Computer science (68-XX) 8 Systems theory; control (93-XX) 6 Approximations and expansions (41-XX) 5 Optics, electromagnetic theory (78-XX) 5 Operations research, mathematical programming (90-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Potential theory (31-XX) 3 Functional analysis (46-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Biology and other natural sciences (92-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX) Citations by Year