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A finite element method using singular functions for Poisson equations: Mixed boundary conditions. (English) Zbl 1124.65108
The purpose of this paper is to extend some results for Dirichlet boundary value problems of Poisson type in the framework of mixed boundary conditions. A singular function representation of the solution is provided for various boundary conditions and a variational problem for the regular part of the solution is derived. Next, the authors introduce a finite element approximation and develop the error analysis. Numerical results conclude this paper and illustrate the main abstract results.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N15 Error bounds for boundary value problems involving PDEs
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