The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions

DOI10.1007/s00211-004-0535-8zbMath1060.65117OpenAlexW2108087611MaRDI QIDQ704804

Ben Qi Guo, Norbert Heuer

Publication date: 19 January 2005

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

Full work available at URL: https://doi.org/10.1007/s00211-004-0535-8

zbMATH Keywords

convergenceSobolev spaceBesov spaceboundary element methodboundary integral equationsLaplace's equationDirichlet and Neumann problemsp-versionweakly singular integral operators2D polygonal domainsenergy normshypersingular operators

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) Boundary element methods for boundary value problems involving PDEs (65N38)

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Cites Work

• The treatment of nonhomogeneous Dirichlet boundary conditions by the p- version of the finite element method
• The \(h\)-\(p\) boundary element method for solving 2- and 3-dimensional problems
• The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
• Multilevel methods for the \(h\)-, \(p\)-, and \(hp\)-versions of the boundary element method
• Schwarz iterations for the efficient solution of screen problems with boundary elements
• Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations
• Optimal estimates for lower and upper bounds of approximation errors in the \(p\)-version of the finite element method in two dimensions
• The \(hp\)-version of the boundary element method on polygons
• 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
• Boundary Integral Operators in Countably Normed Spaces
• Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces
• DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS
• The Optimalp-Version Approximation of Singularities on Polyhedra in the Boundary Element Method
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