Mixed finite element methods for the Rosenau equation

Mixed finite element methods are applied to the Rosenau equation by employing splitting technique. The semi-discrete methods are derived using C0-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0-$$\end{document}piecewise linear finite elements in spatial direction. The existence of unique solutions of the semi-discrete and fully discrete Galerkin mixed finite element methods is proved, and error estimates are established in one space dimension. An extension to problem in two space variables is also discussed. It is shown that the Galerkin mixed finite finite element have the same rate of convergence as in the classical methods without requiring the LBB consistency condition. At last numerical experiments are carried out to support the theoretical claims.