A globally divergence-free weak Galerkin method for Brinkman equations

作者：Zhang, Li^*; Feng, Minfu; Zhang, Jian^*

来源：Applied Numerical Mathematics, 2019, 137: 213-229.

DOI：10.1016/j.apnum.2018.11.002

• Weak Galerkin
• Weak gradient operator
• Brinkman equations
• Globally divergence-free
• Uniform error estimates

In this work, we present and analyze a new weak Galerkin (WG) finite element method for the Brinkman equations. The finite element spaces which are made up of piecewise polynomials are easy to be constructed. Especially, the variational form considered in this work is based on two gradient operators. The stability, priori error estimates and L-2 error estimates for velocity are proved in this paper. In addition, we prove that the new method also yields globally divergence-free velocity approximations. The convergence rates are independent of the Reynolds number, thus the new WG finite element method is efficient for both the Stokes and Darcy equations dominated. Finally, numerical results illustrate the performance of the method and support the theoretical properties of the estimator.

• 单位
  电子科技大学; 四川师范大学; 四川大学