Optimal Error Estimates of A Decoupled Scheme Based on Two-Grid Finite Element for Mixed Stokes-Darcy Model
This work fills a theoretical gap for researchers working on numerical methods for coupled fluid-porous media flow problems.
The paper provides optimal error estimates for a two-grid finite element decoupled scheme for the mixed Stokes-Darcy model, achieving optimal convergence order for velocity and pressure in the fluid region, which was previously only observed numerically.
Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes-Darcy model with Beaver-Joseph-Saffman interface condition in literatures, the numerical analysis only get the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis. By introducing an $H^1-$ orthogonal decomposition of a specific vector valued space, we obtain the optimal error estimates of the velocity and pressure in fluid flow region.