A posteriori error estimates in W^1,p × L^p spaces for the Stokes system with Dirac measures

2019/12/18 by Francisco Fuica, Felipe Lepe, Fuica, Francisco +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1912.08325

openalex publication_date 2019/12/18 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

We design and analyze a posteriori error estimators for the Stokes system with singular sources in suitable W^1,p× L^p spaces. We consider classical low-order inf-sup stable and stabilized finite element discretizations. We prove, in two and three dimensional Lipschitz, but not necessarily convex polytopal domains, that the devised error estimators are reliable and locally efficient. On the basis of the devised error estimators, we design a simple adaptive strategy that yields optimal experimental rates of convergence for the numerical examples that we perform.

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