TY - JOUR
T1 - A Weak Galerkin Method for the Coupled Darcy-Stokes Problem with a Nonstandard Transmission Condition on the Stokes Boundary
AU - Zhao , Jingjun
AU - Lv , Zhiqiang
AU - Xu , Yang
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 29
EP - 52
PY - 2025
DA - 2025/01
SN - 15
DO - http://doi.org/10.4208/eajam.2023-034.260923 
UR - https://global-sci.org/intro/article_detail/eajam/23740.html
KW - Coupled Darcy-Stokes problem, variational inequality, weak Galerkin method, error estimate.
AB - <p style="text-align: justify;">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.</p>