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A Weak Galerkin Method for the Coupled Darcy-Stokes Problem with a Nonstandard Transmission Condition on the Stokes Boundary

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.

Author Details

Jingjun Zhao

Zhiqiang Lv

Yang Xu