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BEM-based Finite Element Approaches on Polytopal Meshes pp 107–140Cite as

Boundary Integral Equations and Their Approximations

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 130))

Abstract

The local problems in the definition of basis functions for the BEM-based FEM are treated by means of boundary integral equations. This chapter gives a short introduction into this topic with a special emphasis on its application in the BEM-based FEM. Therefore, the boundary integral operators for the Laplace problem are reviewed in two- and three-dimensions and corresponding boundary integral equations are derived. Their discretization is realized by a Galerkin boundary element method, which is used in the numerical examples and tests throughout the book. However, we also give an alternative approach for the discretization of boundary integral equations that relies on the Nyström method. The application of these approaches as local solvers for the BEM-based FEM is discussed in details and some comparisons highlighting advantageous and disadvantageous of these two solvers are given.

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Authors and Affiliations

  1. FR Mathematik, Universität des Saarlandes, Saarbrücken, Germany

    Steffen Weißer

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  1. Steffen Weißer
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Weißer, S. (2019). Boundary Integral Equations and Their Approximations. In: BEM-based Finite Element Approaches on Polytopal Meshes. Lecture Notes in Computational Science and Engineering, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-030-20961-2_4

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