TY - JOUR
T1 - A 3D Conforming-Nonconforming Mixed Finite Element for Solving Symmetric Stress Stokes Equations
AU - Min Zhang & Shangyou Zhang
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 730
EP - 743
PY - 2017
DA - 2017/08
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10058.html
KW - Mixed finite element, symmetric stress, Korn's inequality, Stokes equations.
AB - <p style="text-align: justify;">We propose a 3D conforming-nonconforming mixed finite element for solving symmetric
stress Stokes equations. The low-order conforming finite elements are not inf-sup stable. The
low-order nonconforming finite elements do not satisfy the Korn inequality. The proposed finite
element space consists of two conforming components and one nonconforming component. We
prove that the discrete inf-sup condition is valid and the discrete Korn inequality holds uniformly
in the mesh-size. Based on these results we give some numerical verification. In addition, this
element is compared numerically with six other mixed finite elements.</p>