A viscosity-independent error estimate of a pressure-stabilized Lagrange-Galerkin scheme for the Oseen problem

TL;DR

This paper presents a pressure-stabilized Lagrange-Galerkin scheme for the transient Oseen problem that provides viscosity-independent error estimates for velocity approximation, demonstrating high accuracy in low-viscosity scenarios.

Contribution

The paper introduces a novel pressure-stabilized Lagrange-Galerkin scheme with viscosity-independent error bounds for the Oseen problem using equal-order approximation.

Findings

Error estimate for velocity independent of viscosity

Numerical examples confirm high accuracy for small viscosity

Scheme uses equal-order approximation with pressure stabilization

Abstract

We consider a pressure-stabilized Lagrange-Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order $k$ for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the velocity with a constant independent of the viscosity if the exact solution is sufficiently smooth. Numerical examples show high accuracy of the scheme for problems with small viscosity.