A posteriori error analysis for a new fully-mixed isotropic discretization of the stationary Stokes-Darcy coupled problem

TL;DR

This paper presents an a posteriori error analysis for a new stabilized mixed finite element discretization of the stationary Stokes-Darcy coupled problem, ensuring reliable and efficient error estimation on isotropic meshes.

Contribution

It introduces a novel a posteriori error estimator for a fully mixed discretization of the Stokes-Darcy problem, validated for reliability and efficiency.

Findings

The error estimator is proven to be reliable.

The error estimator is proven to be efficient.

The method applies to isotropic meshes in 2D and 3D.

Abstract

In this paper we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming finite element method on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a new robust stabilized fully mixed discretization developed by Jiaping Yu et al. (Advances in Difference Equations, SpringerOpen Journal, 2018). The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution plus the stabilization terms. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.