Analysis Of H ¹ -Galerkin Mixed Finite Element Method For The Rosenau Equation Using Three Intermediate Variables

In this paper, an H 1 - Galerkin mixed finite element method for the fourth order Rosenau equation is studied, where three auxiliary variables are introduced as intermediate functions, which split the equation into four first order equations. Further an appropriate weak formulation is chosen for all the equations. In both semi-discrete and fully-discrete analysis, optimal error estimates are obtained. Furthermore, numerical experiments are used to validate the effectiveness of the method. In this method optimal error estimates of the unknown variable, it’s first derivative, second derivative and the third derivative are obtained simultaneously, which is an added advantage.