A posteriori error estimates for the stationary Navier Stokes equations\n with Dirac measures

2019/10/09 by Alejandro Allendes, Allendes, Alejandro, Enrique Otárola +3
Engineering · Mathematics · #35Q30 #35Q35 #35R06 #65N15 #65N30 #65N50 #76Dxx #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.05122

openalex publication_date 2019/10/09 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

In two dimensions, we propose and analyze an a posteriori error estimator for\nfinite element approximations of the stationary Navier Stokes equations with\nsingular sources on Lipschitz, but not necessarily convex, polygonal domains.\nUnder a smallness assumption on the continuous and discrete solutions, we prove\nthat the devised error estimator is reliable and locally efficient. We\nillustrate the theory with numerical examples.\n

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