D’Angelo, Carlo 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 SIAM J. Numer. Anal. 50, No. 1, 194-215 (2012). 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. Reviewer: Pavol Chocholatý (Bratislava) Cited in 1 ReviewCited in 42 Documents 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 Keywords:elliptic problems; Dirac measure; weighted spaces; finite element method; graded mesh; error estimates; reduced models; multiscale models; microcirculation; stability; convergence; fluid flow in porous media PDFBibTeX XMLCite \textit{C. D'Angelo}, SIAM J. Numer. Anal. 50, No. 1, 194--215 (2012; Zbl 1246.65215) Full Text: DOI