Generalized weak Galerkin finite element method for linear elasticity interface problems

A generalized weak Galerkin finite element method for linear elasticity interface problems is presented. The generalized weak gradient (divergence) is consisted of classical gradient (divergence) and the solution of local problem. Thus, the finite element space can be extended to arbitrary combination of piecewise polynomial spaces. The error equation and error estimates are proved. The numerical results illustrate the efficiency and flexibility for different interfaces, partitions and combinations, the locking-free property, the well performance for low regularity solution in discrete energy, L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2$$\end{document} and L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>{\infty }$$\end{document} norms. Meanwhile, we present the numerical comparison between our algorithm and the weak Galerkin finite element algorithm to demonstrate the flexibility of our algorithm. In addition, for some cases, the convergence rates in numerical tests are obviously higher than the theoretical prediction for the smooth and low regularity solutions.