Space—time CESE method for the convection equation

Abstract

In the paper, we study the analytic convergence of the space-time conservation element and solution element method for smooth solutions of the convection equation. Stability of the method is limited by the CFL condition and a parameter,e,which controls the numerical dissipation. We show that the method converges under appropriate conditions on the mesh and on the parameter,e, by considering a one-dimensional convection equation. The main advantage of this second order scheme is that it is an explicit marching scheme that allows one to solve for both the function and its derivative at the same time with comparable accuracy.Numerical simulations are presented to verify the convergence results for both the linear convection equation and a non-linear conservation law.

Keywords:

• Consevation element-solution element method
• Convection equation
• Comservation laws
• a-e scheme

AMS Subject Classification:

• 65M06
• 65M12

^∗Corresponding author.

^∗Corresponding author.

Notes

^∗Corresponding author.