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) − $P_k (k ≥ 3)$ polynomial tensors enriched with higher order bubbles so as to allow mass lumping, and the displacement field is approximated by $C^{−1}− P_{k−1}$ 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 $L^2$ 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.