Boundary Element Methods: Foundation and Error Analysis

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Abstract
This chapter gives an expository introduction to the Galerkin‐BEM for the elliptic boundary value problems from the mathematical point of view. Emphasis will be placed on the variational formulations of the boundary integral equations and the general error estimates for the approximate solution in appropriate Sobolev spaces. A classification of boundary integral equations will be given on the basis of the Sobolev index. The simple relations between the variational formulations of the boundary integral equations and the corresponding partial differential equations under consideration will be indicated. Basic concepts such as stability, consistency, and convergence, as well as the condition numbers and ill‐posedness, will be discussed by using elementary examples.

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