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Finite element approximation of elliptic problems with Dirac measure terms in weighted spaces: applications to one- and three-dimensional coupled problems. (English) Zbl 1246.65215
This paper deals with the stability and the convergence rates of the finite element approximation of elliptic problems involving Dirac measures. In order to verify the theoretical estimates the author searches the standard finite element solution on uniform and graded meshes and reported the errors in different weighted norms. Also an approach to apply the theoretical results to certain coupled problems involving fluid flow in porous three-dimensional media with one-dimensional fractures is presented.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
76M10 Finite element methods applied to problems in fluid mechanics
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