Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 227-250.
Published online: 2022-02
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0055}, url = {http://global-sci.org/intro/article_detail/nmtma/20228.html} }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.