Local error analysis for the Stokes equations with a punctual source term
type: Item
instance of: scholarly article
title: Local error analysis for the Stokes equations with a punctual source term
zbMATH Open document ID: 1433.65278
author: A. Decoene
author: Loïc Lacouture
author: Sébastien Martin
author: Silvia Bertoluzza
published in: Numerische Mathematik
publication date: 2018-10-31T00:00:00Z
review text: The paper concerns local error analysis for the Stokes equations with a punctual source term. The authors establish in dimension 2 local error estimates for the Stokes problem with a punctual force in source term, and show a quasioptimal convergence in the \(H^1\times L^2\)-norm for a \(P_k/P_{k-1}\)-finite element method, \(k>=2\), and for the \(P_1b/P_1\). The proof is based on local Arnold and Liu error estimates, a weak version of the Aubin-Nitsche duality lemma applied to the Stokes problem and discrete inf-sup conditions. These theoretical results are generalized to a wide class of finite element methods.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 6969647
zbMATH Keywords: local error estimate
zbMATH Keywords: Stokes equations
zbMATH Keywords: punctual source
reviewed by: Xue Jiang
MaRDI profile type: Publication
full work available at URL: s00211-018-0976-0
OpenAlex ID: W2784228261
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Wikidata QID: Q129597890
DOI: 10.1007/S00211-018-0976-0
description: scientific article; zbMATH DE number 6969647