论文标题
高阶混合有限元素，具有质量大块的三角形网格的弹性
High order mixed finite elements with mass lumping for elasticity on triangular grids
论文作者
论文摘要
提出了一个符合三角形网格上质量大块的混合有限元的家族，以实现线性弹性。应力场由对称$ h（{\ rm div}）-p_k（k \ geq 3）$ p_k（k \ geq 3）$多项式张量富含高阶气泡，从而允许质量隆起，可以将其视为具有更高级别的Interior Interior Interior Interior气泡功能。位移字段由$ c^{ - 1} -p_ {k-1} $ polyenmial载体近似，富含高阶术语，以确保稳定性条件。对于所提出的混合元素及其质量集体方案，以$ h（\ rm div）$ norm和$ l^2 $ norm的位移得出了压力的最佳误差估计。数值结果证实了理论分析。
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 $H({\rm div})-P_k (k\geq 3)$ polynomial tensors enriched with higher order bubbles so as to allow mass lumping, which can be viewed as the Hu-Zhang elements enriched with higher order interior bubble functions. The displacement field is approximated by $C^{-1}-P_{k-1}$ polynomial vectors enriched with higher order terms to ensure the stability condition. For both the proposed mixed elements and their mass lumping schemes, optimal error estimates are derived for the stress with $H(\rm div)$ norm and the displacement with $L^2$ norm. Numerical results confirm the theoretical analysis.
