Numerical methods for the rosenau equation

Abstract

In this paper, a continuous in time finite element Galerkin method is first discussed for a KdV-like Rosenau equation in several space variables and optimal error estimates in L², H¹ as well as in H²- norms are derived for conforming C¹-finite element spaces. Finally, several fully discrete schemes like backward Euler, Crank-Nicolson and two step backward methods are proposed and related convergence results are established.

Keywords:

• Finite element method
• conforming C¹-elements
• Rosenau equation
• semidiscrete schemes
• backward Euler
• two step backward and Crank-Nicolson methods
• optimal error estimates

AMS:

• 65M60
• 65M12