Computational study demonstrates optimal error estimates for high-order mixed finite elements with mass lumping in linear elasticity, highlighting efficient stress and displacement approximations.
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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Yang et al. (2022) studied this question.
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