Adaptive boundary element methods for optimal convergence of point errors

DOI10.1007/s00211-015-0727-4zbMath1338.65259OpenAlexW764222646MaRDI QIDQ5964945

Dirk Praetorius, Michael Feischl, Alexander Haberl, Gregor Gantner, Thomas Führer

Publication date: 2 March 2016

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-015-0727-4

zbMATH Keywords

algorithmboundary element methoderror boundLaplaciannumerical resultadaptive mesh-refiningquasi-optimal convergenceweakly-singular integral equation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Complexity and performance of numerical algorithms (65Y20) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items

Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs ⋮ Adaptive FEM for Parameter-Errors in Elliptic Linear-Quadratic Parameter Estimation Problems ⋮ Goal-oriented adaptive finite element methods with optimal computational complexity ⋮ Plain convergence of goal-oriented adaptive FEM ⋮ Research on the recognition algorithm concerning geometric boundary regarding heat conduction based on BEM and CGM ⋮ Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra ⋮ Instance-optimal goal-oriented adaptivity ⋮ Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations ⋮ An Abstract Analysis of Optimal Goal-Oriented Adaptivity ⋮ Optimal convergence rates for goal-oriented FEM with quadratic goal functional

Uses Software

• BEM++
• HILBERT

Cites Work

• Unnamed Item
• Axioms of adaptivity
• On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection
• HILBERT -- a MATLAB implementation of adaptive 2D-BEM. \(\underline {\text H}\)ilbert \(\underline {\text I}\)s a \(\underline {\text L}\)ovely \(\underline {\text B}\)oundary \(\underline {\text E}\)lement \(\underline {\text R}\)esearch \(\underline {\text T}\)ool
• Boundary integral equations
• Adaptive finite element methods with convergence rates
• Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation
• Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation
• Adaptive boundary element methods with convergence rates
• Optimality of a standard adaptive finite element method
• Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method
• Primer of Adaptive Finite Element Methods
• Weighted Marking for Goal-oriented Adaptive Finite Element Methods
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• A Goal-Oriented Adaptive Finite Element Method with Convergence Rates
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Solving Boundary Integral Problems with BEM++
• Local inverse estimates for non-local boundary integral operators
• Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods
• An a posteriori error estimate for a first-kind integral equation
• Boundary Element Methods
• A posteriori error estimate and h-adaptive algorithm on surfaces from Symm's integral equation