An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations

doi:10.1007/s42967-024-00438-2

Abstract

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

CLC Number:

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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