Continuous mixed finite elements for the second order elliptic equation with a low order term

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:357

Article

Huang, Yunqing¹  Li, Jichun²  Zhang, Shangyou³ 

[1] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China

[2] Univ Nevada, Dept Math Sci, 4505 Maryland Pkwy,Box 454020, Las Vegas, NV 89154 USA

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

关键词: Continuous mixed finite element;    Triangular grid;    Tetrahedral grid;   

DOI  :  10.1016/j.cam.2019.02.033

来源: Elsevier

【 摘 要 】

We propose a mixed finite element, where the velocity (in terms of Darcy's law) is approximated by the continuous P-k Lagrange elements and the pressure (the prime variable) is approximated by the discontinuous Pk-t elements, for solving the second order elliptic equation with a low-order term. We show the quasi-optimality for this mixed finite element method. When a low order term is present, the traditional inf-sup condition is no longer required. But the inclusion condition, that the divergence of the discrete velocity space is a subspace of the discrete pressure space, is required. Thus the Taylor-Hood element and most other continuous-pressure mixed elements do not converge. Numerical tests are provided on the new elements and most other popular mixed elements. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free