A Weighted Setting for the Numerical Approximation of the Poisson Problem with Singular Sources

DOI10.1137/18M1213105zbMath1447.65135arXiv1809.03529OpenAlexW3004756591MaRDI QIDQ5215528

Irene Drelichman, Ricardo G. Durán, Ignacio Ojea

Publication date: 12 February 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.03529

zbMATH Keywords

weighted Sobolev spacesfinite element methodsPoisson problem

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) A priori estimates in context of PDEs (35B45) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items

On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra ⋮ Discontinuous Galerkin approximations to elliptic and parabolic problems with a Dirac line source ⋮ Numerical Discretization of a Darcy-Forchheimer Problem Coupled with a Singular Heat Equation ⋮ Global and Local Pointwise Error Estimates for Finite Element Approximations to the Stokes Problem on Convex Polyhedra ⋮ Fully discrete pointwise smoothing error estimates for measure valued initial data ⋮ Anisotropic regularity for elliptic problems with Dirac measures as data ⋮ Ana posteriorierror analysis for an optimal control problem with point sources ⋮ A Posteriori Error Estimates for the Stationary Navier--Stokes Equations with Dirac Measures ⋮ The stationary Boussinesq problem under singular forcing ⋮ Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources ⋮ Stability of the Stokes projection on weighted spaces and applications

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