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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 1515-1528
• 页数: 14页
• 语种: 英文
• DOI: 10.1007/s11425-016-0354-8

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.