An absolutely stable weak Galerkin finite element method for the Darcy–Stokes problem

Xiuli Wang, Qilong Zhai, Ruishu Wang and Rabeea Jari

Applied Mathematics and Computation, 2018, vol. 331, issue C, 20-32

Abstract: In this paper, we apply the weak Galerkin (WG) finite element method to the Darcy–Stokes equations. This method provides accurate approximations for the velocity and the pressure variables. General polygonal or polyhedral partitions can be applied in this method. The finite element space which is made up of piecewise polynomials is easy to be constructed. These advantages make the weak Galerkin finite element method efficient and highly flexible. Optimal rates of convergence for the velocity function u and the pressure function p are established in corresponding norms. In addition, the convergence rates are independent of the viscosity parameter ϵ. Several numerical experiments are provided to illustrate the robustness, flexibility and validity of the weak Galerkin finite element method.

Keywords: Weak Galerkin finite element method; Darcy–Stokes equation; Discrete weak gradient; Discrete weak divergence (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:331:y:2018:i:c:p:20-32

DOI: 10.1016/j.amc.2018.02.034

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