Galerkin Residuals for Adaptive Symmetric-Galerkin Boundary Element Methods

Abstract

This paper presents a simple a posteriori error estimator and an effective adaptive mesh refinement procedure for the symmetric Galerkin boundary element method. The “hypersingular residuals,” developed for error estimation in a standard collocation BEM, are extended to the symmetric Galerkin setting. This leads to the formulation of “Galerkin residuals,” which are intrinsic to the symmetric Galerkin boundary integral approach and form the basis of the present error estimation scheme. Several computational experiments are conducted to test both the accuracy and the reliability of the proposed technique. These experiments involve potential theory and various problem configurations including mixed boundary conditions, corners, and nonconvex domains. The numerical results indicate that reliable solutions to practical engineering problems can be obtained with this method.