Reduced Basis Finite Element Methods for the Korteweg-de Vries-Burgers Equation

Abstract

In this paper, the B-spline Galerkin finite element method and reduced order method for the Korteweg-de Vries-Burgers equation are considered. The semi-discrete and the fully discrete schemes are both provided. The reduced order model of the Korteweg-de Vries-Burgers equation by using proper orthogonal decomposition are provided. The stability and the error estimates of the corresponding schemes are then analyzed. Finally, numerical simulations are presented to show the efficiency of our proposed methods.