TY - JOUR
T1 - A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations
AU - He , Kai
AU - Chen , Junjie
AU - Zhang , Li
AU - Ran , Maohua
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 459
EP - 475
PY - 2024
DA - 2024/06
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1018
UR - https://global-sci.org/intro/article_detail/ijnam/23198.html
KW - Stabilizer-free, weak Galerkin finite element method, Darcy-Stokes equations, weak gradient operator, optimal order error estimates.
AB - <p style="text-align: justify;">In this paper, we propose a new method for the Darcy-Stokes equations based on
the stabilizer-free weak Galerkin finite element method. In the proposed method, we remove the
stabilizer term by increasing the degree of polynomial approximation space of the weak gradient
operator. Compared with the classical weak Galerkin finite element method, it will not increase
the size of global stiffness matrix. We show that the new algorithm not only has a simpler formula,
but also reduces the computational complexity. Optimal order error estimates are established for
the corresponding numerical approximation in various norms. Finally, we numerically illustrate
the accuracy and convergence of this method.</p>