The Penalty Cell-Centered Finite Element Scheme For Stokes Problem On General Meshes

TL;DR

This paper introduces a penalty cell-centered finite element scheme for solving stationary Stokes problems on general meshes, providing rigorous mathematical analysis including existence, uniqueness, and convergence of the scheme.

Contribution

The paper develops and analyzes a novel pFECC scheme for Stokes problems on general meshes, with proofs of key mathematical properties.

Findings

Existence and uniqueness of the discrete solution established.

The stiffness matrix is shown to be symmetric and positive definite.

Convergence of the pFECC scheme is proven.

Abstract

The paper is devoted to the penalty cell-centered finite element scheme (pFECC)on general meshes for the stationary Stokes problems with an incompressible variable viscosity and Dirichlet boundary conditions. In the objectives of this work, we show the rigorous mathematical analysis including the existence, the uniqueness of a discrete solution of the problem, the symmetric and the positive definite stiffness matrix, convergence of the pFECC scheme.