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 -