A weighted setting for the numerical approximation of the Poisson problem with singular sources

I. DRELICHMAN; I. OJEA; R. G. DURÁN

SIAM JOURNAL ON NUMERICAL ANALYSIS

SIAM PUBLICATIONS

Lugar: Philadelphia-USA; Año: 2020 vol. 58 p. 590 - 606

0036-1429

We consider the approximation of Poisson type problems where the source is givenby a singular measure and the domain is a convex polygonal or polyhedral domain. First, weprove the well-posedness of the Poisson problem when the source belongs to the dual of a weightedSobolev space where the weight belongs to the Muckenhoupt class. Second, we prove the stability inweighted norms for standard finite element approximations under the quasi-uniformity assumptionon the family of meshes.