A New Cubic Nonconforming Finite Element on Rectangles

作者：Meng Zhaoliang^*; Luo Zhongxuan; Sheen Dongwoo

来源：Numerical Methods for Partial Differential Equations, 2015, 31(3): 691-705.

DOI：10.1002/num.21911

• nonconforming finite element
• optimal error estimates
• quadrilateral mesh

A new nonconforming rectangle element with cubic convergence for the energy norm is introduced. The degrees of freedom (DOFs) are defined by the 12 values at the three Gauss points on each of the four edges. Due to the existence of one linear relation among the above DOFs, it turns out the DOFs are 11. The nonconforming element consists of . We count the corresponding dimension for Dirichlet and Neumann boundary value problems of second-order elliptic problems. We also present the optimal error estimates in both broken energy and norms. Finally, numerical examples match our theoretical results very well.

• 出版日期2015-5
• 单位大连理工大学