A Weak Galerkin Method for the Coupled Darcy-Stokes Problem with a Nonstandard Transmission Condition on the Stokes Boundary
Year: 2025
Author: Jingjun Zhao, Zhiqiang Lv, Yang Xu
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 1 : pp. 29–52
Abstract
In this paper, we study a coupled problem of Darcy’s law and Stokes equation with nonlinear slip boundary conditions. We derive a variational inequality for the coupled problem in detail. Then we introduce and analyze a weak Galerkin method to solve the coupled problem numerically. Under proper regularity assumptions, we obtain the optimal error estimate $\mathscr{O}(h)$ in newly defined $h$-norms. Finally, we give some numerical results to support the theoretical conclusions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-034.260923
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 1 : pp. 29–52
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Coupled Darcy-Stokes problem variational inequality weak Galerkin method error estimate.