A finite element method by patch reconstruction for the Stokes problem using mixed formulations

TL;DR

This paper introduces a flexible finite element method using patch reconstruction and interior penalty discontinuous Galerkin formulation for solving the Stokes problem, demonstrating stability and efficiency through numerical tests.

Contribution

It presents a novel patch reconstruction finite element approach with stability verified by inf-sup tests, applicable to various velocity-pressure spaces.

Findings

Method shows stability in inf-sup tests.

Numerical examples confirm applicability.

Approach is efficient and flexible.

Abstract

In this paper, we develop a patch reconstruction finite element method for the Stokes problem. The weak formulation of the interior penalty discontinuous Galerkin is employed. The proposed method has a great flexibility in velocity-pressure space pairs whose stability properties are confirmed by the inf-sup tests. Numerical examples show the applicability and efficiency of the proposed method.