Adaptive Boundary Element Method
Adaptive Boundary Element Method
Disciplines
Mathematics (90%); Physics, Astronomy (10%)
Keywords
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Boundary Integral Equations
For two reasons, fast and accurate error estimation plays a key role in reliable and efficient scientific computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. Second, if this is not the case, one aims to improve the discretization, e.g., by local refinement of the underlying mesh. Both subjects are usually covered by so-called a posteriori error estimates and related adaptive mesh-refining algorithms. For error control in finite element methods (FEM), there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive algorithms is well studied in the literature. This is in sharp contrast to the boundary element method (BEM), where only few a posteriori error estimators have been proposed. Moreover, even convergence of adaptive BEM is widely open. Finally, unlike the FEM, most a posteriori error estimators for BEM are computationally expensive and even implementationally challenging. The aim of the project is therefore threefold: First, to give a fair numerical comparison between the error estimators and adaptive mesh-refining algorithms proposed in the BEM literature. Second, to develop a posteriori error estimators in the context of BEM which are numerically cheap to compute. Third, to study the convergence and the optimality of associated adaptive algorithms.
For two reasons, fast and accurate error estimation plays a key role in reliable and efcient scientic computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. Second, if this is not the case, one aims to improve the discretization, e.g., by local renement of the underlying mesh. Both subjects are usually covered by so-called a posteriori error estimates and related adaptive mesh-rening algorithms. For error control in nite element methods, there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive algorithms is well studied in the literature. For integral equations, the funded research project derived a posteriori error estimates and developed and analyzed optimal adaptive mesh-renement strategies.
- Technische Universität Wien - 100%
- Christoph Ortner, University of British Columbia - Canada
- Norbert Heuer, Pontificia Universidad Catolica de Chile - Chile
- Carsten Carstensen, Humboldt-Universität zu Berlin - Germany
- Ernst-Peter Stephan, Universität Hannover - Germany
- Stefan Funken, Universität Ulm - Germany
Research Output
- 1139 Citations
- 66 Publications
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2016
Title Efficient numerical computation of direct exchange areas in thermal radiation analysis DOI 10.1080/10407790.2016.1173469 Type Journal Article Author Feischl M Journal Numerical Heat Transfer, Part B: Fundamentals Pages 511-533 -
2017
Title Local inverse estimates for non-local boundary integral operators DOI 10.1090/mcom/3175 Type Journal Article Author Aurada M Journal Mathematics of Computation Pages 2651-2686 Link Publication -
2012
Title Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems DOI 10.1051/m2an/2011075 Type Journal Article Author Aurada M Journal ESAIM: Mathematical Modelling and Numerical Analysis Pages 1147-1173 Link Publication -
2011
Title Residual a-posteriori error estimates in BEM: convergence of h-adaptive algorithms. Type Conference Proceeding Abstract Author Feischl M Conference Proceedings of IABEM 2011 Conference, Brescia -
2011
Title Convergence of adaptive FEM for elliptic obstacle problems DOI 10.1002/pamm.201110373 Type Journal Article Author Feischl M Journal PAMM Pages 767-768 Link Publication -
2011
Title Efficient implementation of adaptive P1-FEM in Matlab DOI 10.2478/cmam-2011-0026 Type Journal Article Author Funken S Journal Computational Methods in Applied Mathematics Pages 460-490 -
2014
Title On a decoupled linear FEM integrator for eddy-current-LLG DOI 10.1080/00036811.2014.916401 Type Journal Article Author Le K Journal Applicable Analysis Pages 1051-1067 Link Publication -
2014
Title Axioms of adaptivity DOI 10.1016/j.camwa.2013.12.003 Type Journal Article Author Carstensen C Journal Computers & Mathematics with Applications Pages 1195-1253 Link Publication -
2014
Title Adaptive Boundary Element Methods DOI 10.1007/s11831-014-9114-z Type Journal Article Author Feischl M Journal Archives of Computational Methods in Engineering Pages 309-389 Link Publication -
2014
Title Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data DOI 10.1016/j.cam.2013.06.009 Type Journal Article Author Feischl M Journal Journal of Computational and Applied Mathematics Pages 481-501 Link Publication -
2014
Title Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor DOI 10.1515/cmam-2014-0019 Type Journal Article Author Feischl M Journal Computational Methods in Applied Mathematics Pages 485-508 Link Publication -
2014
Title ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve DOI 10.1016/j.enganabound.2013.10.008 Type Journal Article Author Feischl M Journal Engineering Analysis with Boundary Elements Pages 49-60 Link Publication -
2014
Title Rate optimality of adaptive algorithms. Type Conference Proceeding Abstract Author Carstensen C Conference Proceedings of 11th World Congress on Compututational Mechanics (WCCM XI) -
2013
Title HILBERT — a MATLAB implementation of adaptive 2D-BEM DOI 10.1007/s11075-013-9771-2 Type Journal Article Author Aurada M Journal Numerical Algorithms Pages 1-32 Link Publication -
2014
Title Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations DOI 10.48550/arxiv.1408.2693 Type Other Author Feischl M Link Publication -
2014
Title Multiscale modeling in micromagnetics: Existence of solutions and numerical integration DOI 10.1142/s0218202514500328 Type Journal Article Author Bruckner F Journal Mathematical Models and Methods in Applied Sciences Pages 2627-2662 Link Publication -
2014
Title Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems DOI 10.1137/120897225 Type Journal Article Author Feischl M Journal SIAM Journal on Numerical Analysis Pages 601-625 Link Publication -
2014
Title A posteriori error estimation for adaptive IGA boundary element methods. Type Conference Proceeding Abstract Author Feischl M. Praetorius D Et Al Conference Proceedings of 11th World Congress on Compututational Mechanics (WCCM XI), Barcelona -
2014
Title Optimal preconditioning for the coupling of adaptive finite elements and boundary elements. Type Conference Proceeding Abstract Author Feischl M Conference Proceedings of 11th World Congress on Compututational Mechanics (WCCM XI), Barcelona -
2014
Title Rate optimality of adaptive algorithms: An axiomatic Approach. Type Journal Article Author Carstensen C Journal ECCOMAS Newsletter -
2014
Title Stability of symmetric and nonsymmetric FEM–BEM couplings for nonlinear elasticity problems DOI 10.1007/s00211-014-0662-9 Type Journal Article Author Feischl M Journal Numerische Mathematik Pages 199-223 Link Publication -
2016
Title Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations DOI 10.1007/s10092-016-0190-3 Type Journal Article Author Feischl M Journal Calcolo Pages 367-399 Link Publication -
2013
Title Convergence of adaptive FEM for some elliptic obstacle problem DOI 10.1080/00036811.2011.631916 Type Journal Article Author Page M Journal Applicable Analysis Pages 595-615 -
2013
Title On a decoupled linear FEM integrator for Eddy-current-LLG DOI 10.48550/arxiv.1306.3319 Type Other Author Le K Link Publication -
2013
Title Each H^{1/2}-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in R^d DOI 10.48550/arxiv.1306.5115 Type Other Author Aurada M Link Publication -
2013
Title Convergence and Quasi-Optimality of Adaptive FEM with Inhomogeneous Dirichlet Data DOI 10.48550/arxiv.1306.5100 Type Other Author Feischl M Link Publication -
2013
Title ZZ-type aposteriori error estimators for adaptive boundary element methods on a curve DOI 10.48550/arxiv.1306.5120 Type Other Author Feischl M Link Publication -
2012
Title Estimator reduction and convergence of adaptive BEM DOI 10.1016/j.apnum.2011.06.014 Type Journal Article Author Aurada M Journal Applied Numerical Mathematics Pages 787-801 Link Publication -
2012
Title Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics DOI 10.1007/s00211-012-0454-z Type Journal Article Author Ferraz-Leite S Journal Numerische Mathematik Pages 101-131 Link Publication -
2012
Title A posteriori error estimates for the Johnson–Nédélec FEM–BEM coupling DOI 10.1016/j.enganabound.2011.07.017 Type Journal Article Author Aurada M Journal Engineering Analysis with Boundary Elements Pages 255-266 Link Publication -
2012
Title Convergence of adaptive BEM for some mixed boundary value problem DOI 10.1016/j.apnum.2011.03.008 Type Journal Article Author Aurada M Journal Applied Numerical Mathematics Pages 226-245 Link Publication -
2013
Title MIXED CONFORMING ELEMENTS FOR THE LARGE-BODY LIMIT IN MICROMAGNETICS DOI 10.1142/s0218202513500486 Type Journal Article Author Aurada M Journal Mathematical Models and Methods in Applied Sciences Pages 113-144 -
2013
Title Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods DOI 10.1515/cmam-2013-0010 Type Journal Article Author Aurada M Journal Computational Methods in Applied Mathematics Pages 305-332 -
2013
Title Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D DOI 10.1080/00036811.2012.661045 Type Journal Article Author Erath C Journal Applicable Analysis Pages 1194-1216 -
2013
Title Novel inverse estimates for non-local Operators. Type Conference Proceeding Abstract Author Feischl M Conference Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago de Chile -
2013
Title Axioms of Adaptivity DOI 10.48550/arxiv.1312.1171 Type Other Author Carstensen C Link Publication -
2013
Title Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements DOI 10.48550/arxiv.1311.5782 Type Other Author Feischl M Link Publication -
2013
Title A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equation DOI 10.48550/arxiv.1303.4009 Type Other Author Banas L Link Publication -
2013
Title On the Landau-Lifshitz-Gilbert equation with magnetostriction DOI 10.48550/arxiv.1303.4060 Type Other Author Banas L Link Publication -
2013
Title L2-orthogonal projections onto finite elements on locally refined meshes are H1-stable DOI 10.48550/arxiv.1307.0917 Type Preprint Author Karkulik M Link Publication -
2012
Title Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity DOI 10.1007/s00466-012-0779-6 Type Journal Article Author Aurada M Journal Computational Mechanics Pages 399-419 Link Publication -
2012
Title Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity DOI 10.48550/arxiv.1211.4225 Type Other Author Aurada M Link Publication -
2012
Title Inverse estimates for elliptic boundary integral operators and their application to the adaptive coupling of FEM and BEM DOI 10.48550/arxiv.1211.4360 Type Preprint Author Aurada M Link Publication -
2012
Title Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems DOI 10.48550/arxiv.1212.2620 Type Other Author Feischl M Link Publication -
2012
Title Multiscale modeling in micromagnetics: existence of solutions and numerical integration DOI 10.48550/arxiv.1209.5548 Type Other Author Bruckner F Link Publication -
2012
Title On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H1-Stability of L2-Projection DOI 10.48550/arxiv.1210.0367 Type Other Author Karkulik M Link Publication -
2012
Title Convergence of adaptive boundary element methods DOI 10.1216/jie-2012-24-1-1 Type Journal Article Author Carstensen C Journal Journal of Integral Equations and Applications Pages 1-23 Link Publication -
2012
Title Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems DOI 10.48550/arxiv.1210.8369 Type Other Author Feischl M Link Publication -
2012
Title Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data DOI 10.48550/arxiv.1207.3257 Type Other Author Feischl M Link Publication -
2011
Title Adaptive coupling of FEM and BEM: Simple error estimators and convergence DOI 10.1002/pamm.201110367 Type Journal Article Author Aurada M Journal PAMM Pages 755-756 -
2011
Title Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data DOI 10.1002/pamm.201110374 Type Journal Article Author Feischl M Journal PAMM Pages 769-772 Link Publication -
2013
Title FEM-BEM couplings without stabilization. Type Conference Proceeding Abstract Author Feischl M Conference Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago de Chile -
2013
Title Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement DOI 10.1002/num.21792 Type Journal Article Author Karkulik M Journal Numerical Methods for Partial Differential Equations Pages 2081-2106 -
2013
Title Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd DOI 10.1051/m2an/2013069 Type Journal Article Author Aurada M Journal ESAIM: Mathematical Modelling and Numerical Analysis Pages 1207-1235 Link Publication -
2013
Title Quasi-optimal adaptive BEM. Type Conference Proceeding Abstract Author Feischl M Conference Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago de Chile -
2013
Title On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H1-Stability of L2-Projection DOI 10.1007/s00365-013-9192-4 Type Journal Article Author Karkulik M Journal Constructive Approximation Pages 213-234 Link Publication -
2013
Title Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, part I: weakly-singular integral equation DOI 10.1007/s10092-013-0100-x Type Journal Article Author Feischl M Journal Calcolo Pages 531-562 -
2013
Title Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method DOI 10.1137/110842569 Type Journal Article Author Feischl M Journal SIAM Journal on Numerical Analysis Pages 1327-1348 -
2008
Title Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method DOI 10.1137/07069047x Type Journal Article Author Cascon J Journal SIAM Journal on Numerical Analysis Pages 2524-2550 Link Publication -
2015
Title Simultaneous quasi-optimal convergence rates in FEM-BEM coupling DOI 10.1002/mma.3374 Type Journal Article Author Melenk J Journal Mathematical Methods in the Applied Sciences Pages 463-485 Link Publication -
2015
Title Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations DOI 10.1016/j.cma.2015.03.013 Type Journal Article Author Feischl M Journal Computer Methods in Applied Mechanics and Engineering Pages 362-386 Link Publication -
2015
Title Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements DOI 10.1002/num.22025 Type Journal Article Author Feischl M Journal Numerical Methods for Partial Differential Equations Pages 603-632 Link Publication -
2015
Title FEM–BEM coupling for the large-body limit in micromagnetics DOI 10.1016/j.cam.2014.11.042 Type Journal Article Author Aurada M Journal Journal of Computational and Applied Mathematics Pages 10-31 Link Publication -
2015
Title Quasi-optimal convergence rates for adaptive boundary element methods with data approx- imation - Part II: Hyper-singular integral equation. Type Journal Article Author Feischl M -
2015
Title Energy norm based error estimators for adaptive BEM for hypersingular integral equations DOI 10.1016/j.apnum.2013.12.004 Type Journal Article Author Aurada M Journal Applied Numerical Mathematics Pages 15-35 -
2010
Title Convergence of simple adaptive Galerkin schemes based on h - h/2 error estimators DOI 10.1007/s00211-010-0292-9 Type Journal Article Author Ferraz-Leite S Journal Numerische Mathematik Pages 291-316 Link Publication