Exponential convergence of the \(hp\)-version for the boundary element method on open surfaces

DOI10.1007/s002119900082zbMath0946.65120OpenAlexW2035409961MaRDI QIDQ1964051

Norbert Heuer, Ernst Peter Stephan, Matthias Maischak

Publication date: 10 October 2000

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

Full work available at URL: https://doi.org/10.1007/s002119900082

zbMATH Keywords

exponential convergenceGalerkin boundary element methodweakly singular integral operatorhypersingular operatorpiecewise smooth boundaryopen surfacetensor products of splinesgeometrically refined mesh

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

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Natural hp-BEM for the electric field integral equation with singular solutions ⋮ Anhp-adaptive refinement strategy for hypersingular operators on surfaces ⋮ Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation ⋮ Adaptive Galerkin boundary element methods with panel clustering ⋮ \(hp\)-version time domain boundary elements for the wave equation on quasi-uniform meshes ⋮ The \(p\)-version of the boundary element method for weakly singular operators on piecewise plane open surfaces ⋮ The \(hp\)-version of the boundary element method for Helmholtz screen problems ⋮ Two-level methods for the single layer potential in \(\mathbb{R}^3\) ⋮ Thehp-version of the BEM with quasi-uniform meshes for a three-dimensional crack problem: The case of a smooth crack having smooth boundary curve ⋮ A p‐adaptive algorithm for the BEM with the hypersingular operator on the plane screen ⋮ Discontinuous Galerkin \(hp\)-BEM with quasi-uniform meshes ⋮ Thehp-version of the boundary element method with quasi-uniform meshes in three dimensions ⋮ Exponential convergence of the h–p version BEM for mixed boundary value problems on polyhedrons ⋮ The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: A priori error analysis ⋮ An iterative substructuring method for the hp‐version of the BEM on quasi‐uniform triangular meshes ⋮ The \(p\)-version of the boundary element method for a three-dimensional crack problem ⋮ Multiplicative Schwarz algorithms for the \(p\)-version Galerkin boundary element method in 3D ⋮ The \(hp\)-version of the boundary element method on polygons ⋮ Multilevel methods for the \(h\)-, \(p\)-, and \(hp\)-versions of the boundary element method

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