The \(p\)-version of the boundary element method for a three-dimensional crack problem

DOI10.1216/jiea/1181075334zbMath1095.74047OpenAlexW1998252918MaRDI QIDQ2496918

Norbert Heuer, Alexei Bespalov

Publication date: 25 July 2006

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jiea/1181075334

zbMATH Keywords

convergenceweakly singular operatorquasi-optimal a priori error estimate

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Brittle fracture (74R10) Boundary element methods applied to problems in solid mechanics (74S15) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (5)

\(hp\)-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 ⋮ Higher-order time domain boundary elements for elastodynamics: graded meshes and \textit{hp} versions ⋮ Multiplicative Schwarz algorithms for the \(p\)-version Galerkin boundary element method in 3D ⋮ The boundary element method with Lagrangian multipliers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions
• An improved boundary element Galerkin method for three-dimensional crack problems
• The h-p version of the finite element method. I. The basic approximation results
• The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
• Exponential convergence of the \(hp\)-version for the boundary element method on open surfaces
• The optimal convergence of the \(h\)-\(p\) version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains
• The \(hp\)-version of the boundary element method on polygons
• The \(p\)-version of the boundary element method for hypersingular operators on piecewise plane open surfaces
• Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
• A boundary integral equation method for three‐dimensional crack problems in elasticity
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• On the Convergence of the p-Version of the Boundary Element Galerkin Method
• The $h-p$ version of the boundary element method on polygonal domains with quasiuniform meshes
• The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling
• Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
• The Optimalp-Version Approximation of Singularities on Polyhedra in the Boundary Element Method
• The<scp>h</scp>-<scp>p</scp>Version of the Voundary Element Method for Transmission Problems with Piecewise Analytic Data

This page was built for publication: The \(p\)-version of the boundary element method for a three-dimensional crack problem