A viscosity-independent error estimate of a pressure-stabilized Lagrange-Galerkin scheme for the Oseen problem
Provides a theoretical guarantee for a numerical scheme that handles small viscosity in fluid dynamics, but the result is incremental as it extends existing stabilization techniques.
The paper presents a pressure-stabilized Lagrange-Galerkin scheme for the transient Oseen problem with small viscosity, proving a viscosity-independent error estimate for velocity. Numerical examples demonstrate high accuracy for small viscosity problems.
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.