TY - JOUR
T1 - High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids
AU - Yang , Yan
AU - Xie , Xiaoping
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 227
EP - 250
PY - 2022
DA - 2022/02
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2021-0055
UR - https://global-sci.org/intro/article_detail/nmtma/20228.html
KW - Linear elasticity, mixed finite element, mass lumping, error estimate.
AB - <p style="text-align: justify;">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.</p>