Numerical Analysis of A Mixed Finite Element Method for Rosenau-Burgers Equation

Abstract

Abstract. An H 1 -Galerkin mixed finite element method (H 1 MFEM) is proposed and analyzed for the fourth-order nonlinear Rosenau-Burgers equation. By introducing three auxiliary variables, the first-order system of four equations is formulated. The fully discrete scheme is studied for problem and optimal a priori error estimates for L 2 and H 1 -norms for the scalar unknown, first derivative, second derivative and third derivative are obtained simultaneously.