Abstract

Based on a hierarchical basis a posteriori error estimator, an adaptive weak Galerkin finite element method (WGFEM) is proposed for the Stokes problem in two and three dimensions. In this paper, we propose two novel diagonalization techniques for velocity and pressure, respectively. Using diagonalization techniques, we need only to solve two diagonal linear algebraic systems corresponding to the degree of freedom to get the error estimator. The upper bound and lower bound of the error estimator are also shown to address the reliability of the adaptive method. Numerical simulations are provided to demonstrate the effectiveness and robustness of our algorithm.

Short bio

张佳川，南京工业大学讲师，博士毕业于吉林大学。研究方向主要为偏微分方程数值解以及后验误差估计