High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids
Year: 2022
Author: Yan Yang, Xiaoping Xie
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 1 : pp. 227–250
Abstract
A family of conforming mixed finite elements with mass lumping on triangular grids are presented for linear elasticity. The stress field is approximated by symmetric H(div) − Pk(k≥3) polynomial tensors enriched with higher order bubbles so as to allow mass lumping, and the displacement field is approximated by C−1−Pk−1 polynomial vectors enriched with higher order terms. For both the proposed mixed elements and their mass lumping schemes, optimal error estimates are derived for the stress and displacement in H(div) norm and L2 norm, respectively. Numerical results confirm the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2021-0055
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 1 : pp. 227–250
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Linear elasticity mixed finite element mass lumping error estimate.
Author Details
Yan Yang Email
Xiaoping Xie Email