Boundary Element Methods – An Overview
Date
2004
Authors
Hsiao, George C.
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. This paper gives an overview of the method from both theoretical and numerical point of view. It summaries the main results obtained by the author and his collaborators over the last 30 years. Fundamental theory and various applications will be illustrated through simple examples. Some numerical experiments in elasticity as well as in fluid mechanics will be included to demonstrate the efficiency of the methods.
Description
Dedicated to Professor Dr. Wolfgang L.Wendland in Friendship and Admiration. This
paper is based on a plenary lecture entitled Boundary Element Methods – past, present and
the future, delivered by the author at the First Chilean Workshop on Numerical Analysis
of Partial Differential Equations, Universidal de Concepcion, Chile, January 13-16, 2004.
Keywords
Boundary integral equations , fundamental solutions , variational formulations , Sobolev spaces , weak solutions , Garding’s inequality , Galerkin’s method , boundary elements , stability , ill-posedness , asymptotic error estimates