A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations

A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations

Year:    2024

Author:    Kai He, Junjie Chen, Li Zhang, Maohua Ran

International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 4 : pp. 459–475

Abstract

In this paper, we propose a new method for the Darcy-Stokes equations based on the stabilizer-free weak Galerkin finite element method. In the proposed method, we remove the stabilizer term by increasing the degree of polynomial approximation space of the weak gradient operator. Compared with the classical weak Galerkin finite element method, it will not increase the size of global stiffness matrix. We show that the new algorithm not only has a simpler formula, but also reduces the computational complexity. Optimal order error estimates are established for the corresponding numerical approximation in various norms. Finally, we numerically illustrate the accuracy and convergence of this method.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ijnam2024-1018

International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 4 : pp. 459–475

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Stabilizer-free weak Galerkin finite element method Darcy-Stokes equations weak gradient operator optimal order error estimates.

Author Details

Kai He

Junjie Chen

Li Zhang

Maohua Ran