On Asymptotic Error Analysis and Mathematical Principles for Boundary Element Methods

Abstract

Boundary element methods which can be considered as numerical or finite element approximations of boundary integral equations on closed boundary manifolds became very popular during the last years and, correspondingly,a great variety of boundary value problems can now be solved numerically with corresponding boundary element programs. Since the reduction of interior or exterior boundary value problems and also transmission problems to equivalent boundary integral equations is by no means a uniquely determined process — even for one specific boundary value problem — the growing number of applications has led to an enormous variety of mathematical problems and questions in connection with the applicability, correctness of formulations, systematical and computational errors and their estimation, computing times and expenses and efficiency.