Finite element method and natural boundary reduction. (English) Zbl 0569.65076

Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 1439-1453 (1984).
[For the entire collection see Zbl 0553.00001.]
Most elliptic boundary value problems have equivalent (variational) formulations in forms of integral equations on the boundary. Solving these integral equations in place of the original problem by using the finite element method (boundary element method) has the advantage of dimishing the number of space dimensions by 1, moreover infinite, cornered or cracked domains may be handled; on the other hand complexity in the analytical formulation is increased.
In order to develop boundary element methods as components of finite element methods a natural and direct method of boundary reduction is presented. Laplace equation (Neumann problems), general elliptic equations and Helmholtz equation (Sommerfeld radiation condition at infinity) are discussed.
Reviewer: J.Weisel


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation


Zbl 0553.00001