A Pressure-Robust Weak Galerkin Finite Element Method for Navier-Stokes Equations

TL;DR

This paper introduces a pressure-robust weak Galerkin finite element method for steady incompressible Navier-Stokes equations, ensuring velocity errors are unaffected by pressure and body forces, with proven optimal convergence and validated numerically.

Contribution

The paper presents a novel pressure-robust weak Galerkin scheme for Navier-Stokes equations using divergence-preserving velocity reconstruction, enhancing accuracy and robustness.

Findings

Achieves pressure-robust velocity approximation independent of pressure.

Proves optimal convergence rates through error analysis.

Numerical experiments confirm theoretical results.

Abstract

In this paper, we develop and analyze a novel numerical scheme for the steady incompressible Navier-Stokes equations by the weak Galerkin methods. The divergence-preserving velocity reconstruction operator is employed in the discretization of momentum equation. By employing the velocity construction operator, our algorithm can achieve pressure-robust, which means, the velocity error is independent of the pressure and the irrotational body force. Error analysis is established to show the optimal rate of convergence. Numerical experiments are presented to validate the theoretical conclusions.