Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity

Fleurianne Bertrand, Bernhard Kober, Marcel Moldenhauer, Gerhard Starke

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

Based on the displacement–pressure approximation computed with a stable finite element pair, a stress equilibration procedure for linear elasticity is proposed. Our focus is on the Taylor–Hood finite element space, with emphasis on the behavior for (nearly) incompressible materials. From a combination of displacement in the standard continuous finite element spaces of polynomial degrees k+1 and pressure in the standard continuous finite element spaces of polynomial degrees k, we construct an H(div)-conforming, weakly symmetric stress reconstruction. Explicit formulas are first given for a flux reconstruction and then for the stress reconstruction.
Original languageEnglish
Title of host publicationCISM International Centre for Mechanical Sciences, Courses and Lectures
EditorsJörg Schröder, Paulo de Mattos Pimenta
Place of PublicationSpringer
PublisherSpringer
Pages69-106
ISBN (Electronic)978-3-030-33520-5
ISBN (Print)978-3-030-33519-9
DOIs
Publication statusPublished - 2020
Externally publishedYes

Publication series

NameCISM International Centre for Mechanical Sciences book series (CISM)
PublisherSpringer
Volume597
ISSN (Print)0254-1971
ISSN (Electronic)2309-3706

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