An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations

doi:10.1007/s42967-024-00438-2

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (3): 1016-1033.doi: 10.1007/s42967-024-00438-2

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An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations

Wenya Qi¹, Junping Wang²

1 School of Mathematics and Information Sciences, Henan Normal University, Xinxiang 453007, Henan, China;
2 Division of Mathematical Sciences, U. S. National Science Foundation, Alexandria, VA 22314, USA

收稿日期:2023-11-01 修回日期:2024-03-24 接受日期:2024-06-09 出版日期:2025-09-20 发布日期:2025-05-23
通讯作者: Junping Wang, jwang@nsf.gov;Wenya Qi, qiwymath@163.com E-mail:jwang@nsf.gov;qiwymath@163.com

An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations

Wenya Qi¹, Junping Wang²

1 School of Mathematics and Information Sciences, Henan Normal University, Xinxiang 453007, Henan, China;
2 Division of Mathematical Sciences, U. S. National Science Foundation, Alexandria, VA 22314, USA

Received:2023-11-01 Revised:2024-03-24 Accepted:2024-06-09 Online:2025-09-20 Published:2025-05-23

摘要/Abstract

摘要： An upwind weak Galerkin finite element scheme was devised and analyzed in this article for convection-dominated Oseen equations. The numerical algorithm was based on the weak Galerkin method enhanced by upwind stabilization. The resulting finite element scheme uses equal-order, say k, polynomial spaces on each element for the velocity and the pressure unknowns. With finite elements of order k ≥ 1, the numerical solutions are proved to converge at the rate of O(h^k+$\frac{1}{2}$) in an energy-like norm for convection-dominated Oseen equations. Numerical results are presented to demonstrate the accuracy and effectiveness of the upwind weak Galerkin scheme.

关键词: Convection-dominated, Weak Galerkin, Oseen equations, Upwind schemes

Abstract: An upwind weak Galerkin finite element scheme was devised and analyzed in this article for convection-dominated Oseen equations. The numerical algorithm was based on the weak Galerkin method enhanced by upwind stabilization. The resulting finite element scheme uses equal-order, say k, polynomial spaces on each element for the velocity and the pressure unknowns. With finite elements of order k ≥ 1, the numerical solutions are proved to converge at the rate of O(h^k+$\frac{1}{2}$) in an energy-like norm for convection-dominated Oseen equations. Numerical results are presented to demonstrate the accuracy and effectiveness of the upwind weak Galerkin scheme.

Key words: Convection-dominated, Weak Galerkin, Oseen equations, Upwind schemes

中图分类号:

Wenya Qi, Junping Wang. An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(3): 1016-1033.

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An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations

An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations

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