The weak Galerkin finite element method for Stokes interface problems with curved interface

TL;DR

This paper introduces a novel weak Galerkin finite element method tailored for Stokes interface problems with curved interfaces, achieving optimal convergence rates through theoretical analysis and numerical validation.

Contribution

The paper develops a new weak Galerkin scheme that accurately handles curved interfaces in Stokes problems, incorporating interface conditions directly into the variational formulation.

Findings

Errors reach optimal convergence order under energy norm

Errors reach optimal convergence order under L2 norm

Numerical experiments confirm theoretical results

Abstract

In this paper, we develop a new weak Galerkin finite element scheme for the Stokes interface problem with curved interfaces. We take a unique vector-valued function at the interface and reflect the interface condition in the variational problem. Theoretical analysis and numerical experiments show that the errors can reach the optimal convergence order under the energy norm and $L^2$ norm.