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A posteriori error estimates for elliptic problems with Dirac delta source terms. (English) Zbl 1162.65401

Summary: The aim of this paper is to introduce residual type a posteriori error estimators for a Poisson problem with a Dirac delta source term, in \(L^p\) norm and \(W^{1,p}\) seminorm. The estimators are proved to yield global upper and local lower bounds for the corresponding norms of the error. They are used to guide adaptive procedures, which are experimentally shown to lead to optimal orders of convergence.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Software:

Triangle; na14
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Full Text: DOI

References:

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