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

Jingjun Zhao; Zhiqiang Lv; Yang Xu

doi:10.4208/eajam.2023-034.260923

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

Jingjun Zhao^*
, Zhiqiang Lv
, Yang Xu^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 O (h) in newly defined h-norms. Finally, we give some numerical results to support the theoretical conclusions.

Original language	English
Pages (from-to)	29-52
Number of pages	24
Journal	East Asian Journal on Applied Mathematics
Volume	15
Issue number	1
DOIs	https://doi.org/10.4208/eajam.2023-034.260923
State	Published - 2025
Externally published	Yes

Keywords

Coupled Darcy-Stokes problem
error estimate
variational inequality
weak Galerkin method

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10.4208/eajam.2023-034.260923

Cite this

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

abstract = "In this paper, we study a coupled problem of Darcy{\textquoteright}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 O (h) in newly defined h-norms. Finally, we give some numerical results to support the theoretical conclusions.",

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AU - Zhao, Jingjun

AU - Lv, Zhiqiang

AU - Xu, Yang

PY - 2025

Y1 - 2025

N2 - 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 O (h) in newly defined h-norms. Finally, we give some numerical results to support the theoretical conclusions.

AB - 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 O (h) in newly defined h-norms. Finally, we give some numerical results to support the theoretical conclusions.

KW - Coupled Darcy-Stokes problem

KW - error estimate

KW - variational inequality

KW - weak Galerkin method

UR - https://www.scopus.com/pages/publications/105015213001

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DO - 10.4208/eajam.2023-034.260923

M3 - 文章

AN - SCOPUS:105015213001

SN - 2079-7362

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SP - 29

EP - 52

JO - East Asian Journal on Applied Mathematics

JF - East Asian Journal on Applied Mathematics

IS - 1

ER -

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

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Keywords

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