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A finite element method using singular functions for the Poisson equation: Corner singularities. (English) Zbl 0992.65122

A new finite element method is derived for the Poisson equation with homogeneous Dirichlet boundary data on a polygonal domain with one reentrant corner. A new extraction formula for the stress intensity factor is derived. Error bounds are proven.

MSC:

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