TY - CHAP

T1 - Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity

AU - Bertrand, Fleurianne

AU - Kober, Bernhard

AU - Moldenhauer, Marcel

AU - Starke, Gerhard

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85076763181&partnerID=MN8TOARS

U2 - 10.1007/978-3-030-33520-5_3

DO - 10.1007/978-3-030-33520-5_3

M3 - Chapter

SN - 978-3-030-33519-9

T3 - CISM International Centre for Mechanical Sciences book series (CISM)

SP - 69

EP - 106

BT - CISM International Centre for Mechanical Sciences, Courses and Lectures

A2 - Schröder, Jörg

A2 - de Mattos Pimenta, Paulo

PB - Springer

CY - Springer

ER -