A global H(div)-conforming finite element post-processing for stress recovery in nearly incompressible elasticity

G. Taraschi, M.R. Correa, A.S. Pinto and C.O. Faria

Applied Mathematics and Computation, 2024, vol. 470, issue C

Abstract: In this work, we study the application of a post-processing strategy to recover the stress field in the linear elasticity problem, with a particular interest in the limit of near incompressibility. The developed analysis leads to error bounds for the approximated stress that do not depend on the Lamé coefficient λ, implying that the strategy remains accurate even on nearly-incompressible problems. We also present appropriate H(div)-conforming approximation spaces to guarantee optimal convergence rates on meshes made of triangular or convex quadrilateral elements and comment on the application in meshes of tetrahedra and hexahedra. Finally, we perform numerical tests to illustrate the robustness of the proposed post-processing strategy and verify the theoretical predictions.

Keywords: Linear elasticity; H(div) approximations; Stress post-processing; Mixed finite element methods; Second order elliptic problems; Two and three dimensional approximations (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000596

DOI: 10.1016/j.amc.2024.128587

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