A divergence-free weak Galerkin method for quasi-Newtonian Stokes flows  

作　　者：ZHENG XiaoBo CHEN Gang XIE XiaoPing 

机构地区：[1]School of Mathematics, Sichuan University

出　　处：《Science China Mathematics》2017年第8期1515-1528,共14页中国科学：数学（英文版）

基　　金：supported by Major Research Plan of National Natural Science Foundation of China (Grant No. 91430105)

摘　　要：This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1(k 0) and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k + 1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results.This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k ＋ 1（k 0） and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k ＋ 1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results.

关 键 词：quasi-Newtonian Stokes equation weak Galerkin method DIVERGENCE-FREE optimal error estimate 

分 类 号：O241.82[理学—计算数学]