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On some mathematical aspects of boundary element methods for elliptic problems. (English) Zbl 0587.65079
The mathematics of finite elements and applications V, MAFELAP 1984, Proc. 5th Conf., Uxbridge/Engl. 1984, 193-227 (1985).
[For the entire collection see Zbl 0566.00028.]
This paper gives a survey on the mathematical analysis of boundary element methods (BEM) related to elliptic boundary value problems. The choice of elementary numerical manipulations and the formulation of some of the corresponding mathematical questions are discussed to improve the efficiency of BEM. The postprocessing for the evaluation of the originally sought solution of the boundary value problem and the development and use of efficient fast solvers in BEM are treated to clarify some directions of the work in BEM.
Reviewer: N.F.F.Ebecken

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
35J25 Boundary value problems for second-order elliptic equations
35C15 Integral representations of solutions to PDEs