Local convergence of the boundary element method on polyhedral domains

Abstract

The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm's integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local a priori estimates in $L^2$ for Symm's integral equation and in $H^1$ for the hypersingular equation. The local rate of convergence is limited by the local regularity of the sought solution and the sum of the global regularity and additional regularity provided by the shift theorem for a dual problem.

References in corpus (2)

• Existence of $\mathcal{H}$-matrix approximants to the inverses of BEM matrices: the simple-layer operator
• Existence of $\mathcal{H}$-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator

Cited by in corpus (4)

• Local convergence of the FEM for the integral fractional Laplacian
• Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings
• Numerical analysis on boundary integral equation to exterior Dirichlet problem of Laplace equation
• Unified analysis on Petrov-Galerkin method into Symm's integral of the first kind