A weak Galerkin-mixed finite element method for the Stokes-Darcy problem
Hui Peng, Qilong Zhai, Ran Zhang, Shangyou Zhang
TL;DR
This paper introduces a novel numerical scheme combining weak Galerkin and mixed finite element methods to solve the coupled Stokes-Darcy problem, providing stability and optimal error estimates validated by numerical experiments.
Contribution
It develops a new coupled numerical method for Stokes-Darcy problems with proven stability and error bounds, enhancing computational accuracy.
Findings
Proved a discrete inf-sup condition for the scheme.
Derived optimal error estimates for the method.
Numerical experiments confirm theoretical results.
Abstract
In this paper, we propose a new numerical scheme for the coupled Stokes-Darcy model with Beavers-Joseph-Saffman interface condition. We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to the Darcy equation. A discrete inf-sup condition is proved and optimal error estimates are also derived. Numerical experiments validate the theoretical analysis.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Lattice Boltzmann Simulation Studies · Computational Fluid Dynamics and Aerodynamics