# Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

# Boundary Element Methods

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_18-1

## Definitions

Boundary element method (BEM) is a computational technique for the approximate solution of the problems in continuum mechanics. In BEM the governing differential equations are transformed into equivalent boundary integral equations with the aid of Gauss (divergence) theorem and fundamental solutions.

Fundamental solutions are special type of Green’s functions, which are solutions of the governing equations due to a point force acting in an infinite domain.

## Introduction

The attraction of the boundary element method (BEM) is generally attributed to the reduction in the dimensionality of the problem; for two-dimensional problems, only the line boundary of the domain needs to be discretized into elements (see Fig. 1), and for three-dimensional problems, only the surface of the problem needs to be discretized. In comparison to the finite element method (FEM) and other domain-type analysis techniques, a boundary analysis results in a...
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