A discontinuous Galerkin pressure correction scheme for the Oldroyd model of order one

2025/07/05 by Mondal, Pratyay, Sinha, Rajen Kumar
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2507.03909

Abstract

We develop and analyze a discontinuous Galerkin pressure correction scheme for the Oldroyd model of order one. The existence and uniqueness of the discrete solution as well as the consistency of the scheme are proved. The stability of the discrete velocity and pressure are established. We derive optimal a priori error bounds for the fully discrete velocity in the discontinuous discrete space. In addition, an improved error estimate for the velocity is derived in the L² norm which is optimal with respect to space and time. Furthermore, the error bound for the pressure is obtained via the estimates of discrete time derivative of the velocity. Finally, numerical experiments confirm the optimal convergence rates.

Citations

• Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations
• A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence
• A Stable and High-Order Accurate Discontinuous Galerkin Based Splitting\n Method for the Incompressible Navier-Stokes Equations
• Backward Euler method for the Equations of Motion Arising in Oldroyd Fluids of Order One with Nonsmooth Initial Data
• Discontinuous Galerkin methods for solving elliptic and parabolic equations : theory and implementation
• The Finite Element Method for Elliptic Problems
• Numerical solution of the Navier-Stokes equations

Related

• Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations
• A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence
• Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data
• Optimal Error Estimates of a Discontinuous Galerkin Method for the Navier-Stokes Equations
• Backward Euler method for the Equations of Motion Arising in Oldroyd Fluids of Order One with Nonsmooth Initial Data