Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement
From MaRDI portal
Publication:2864606
DOI10.1002/num.21792zbMath1280.65116OpenAlexW2151758747MaRDI QIDQ2864606
Dirk Praetorius, Günther Of, Michael Karkulik
Publication date: 26 November 2013
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.21792
algorithmconvergencenumerical experimentserror boundsadaptive algorithmfast multipole methoderror reductionmesh-refinement3D Laplacianadaptive boundary element method (BEM)weakly-singular integral formulation
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) Boundary element methods for boundary value problems involving PDEs (65N38)
Related Items (8)
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 ⋮ Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation ⋮ On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection ⋮ A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling ⋮ Block-adaptive cross approximation of discrete integral operators ⋮ Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data ⋮ Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation ⋮ Energy norm based error estimators for adaptive BEM for hypersingular integral equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection
- An adaptive mesh-refining algorithm allowing for an \(H^1\) stable \(L^2\) projection onto Courant finite element spaces
- Simple a posteriori error estimators for the \(h\)-version of the boundary element method
- An introduction to Sobolev spaces and interpolation spaces
- Convergence of simple adaptive Galerkin schemes based on \(h - h/2\) error estimators
- Feedback and adaptive finite element solution of one-dimensional boundary value problems
- Multilevel norms for \(H^{-1/2}\)
- Variable order composite quadrature of singular and nearly singular integrals
- Local a-posteriori error indicators for the Galerkin discretization of boundary integral equations
- Two-level methods for the single layer potential in \(\mathbb{R}^3\)
- A new a posteriori error estimator in adaptive direct boundary element methods: The Dirichlet problem
- Small data oscillation implies the saturation assumption
- Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. II: The three-dimensional case
- Residual-based a posteriori error estimate for hypersingular equation on surfaces
- The fast solution of boundary integral equations.
- On the stability of the $L^2$ projection in $H^1(\Omega)$
- Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for $H^1$-stability of the $L^2$-projection onto finite element spaces
- Exponential convergence ofhpquadrature for integral operators with Gevrey kernels
- Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method
- Artificial Multilevel Boundary Element Preconditioners
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- Parallel Multilevel Preconditioners
- Concepts of an adaptive hierarchical finite element code
- A p‐adaptive algorithm for the BEM with the hypersingular operator on the plane screen
- A posterior error estimates for hp—boundary element methods
- The BPX preconditioner for the single layer potential operator
- Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary elements methods. Part I. The two-dimensional case
- Adaptive Boundary Element Methods Based on Computational Schemes for Sobolev Norms
- Anhp-adaptive refinement strategy for hypersingular operators on surfaces
- Finite elements on degenerate meshes: inverse-type inequalities and applications
- A Posteriori Error Estimates for Boundary Element Methods
- Efficiency of a posteriori BEM–error estimates for first-kind integral equations on quasi–uniform meshes
- Adaptive Boundary Element Mevthods for Some First Kind Integral Equations
- The fast multipole method for the symmetric boundary integral formulation
- An adaptive boundary element method for the exterior Stokes problem in three dimensions
- Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind
- An a posteriori error estimate for a first-kind integral equation
- A fast algorithm for particle simulations
- On the stability of the \(L_2\) projection in fractional Sobolev spaces
- Mathematical foundation of a posteriori error estimates and adaptive mesh-refining algorithms for boundary integral equations of the first kind
- A posteriori error estimate and h-adaptive algorithm on surfaces from Symm's integral equation
- \(hp\)-adaptive two-level methods for boundary integral equations on curves
This page was built for publication: Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement
