Mixed finite element methods for a fourth order reaction diffusion equation

Abstract

AbstractMixed finite element methods are applied to a fourth order reaction diffusion equation with different types of boundary conditions. Some a priori bounds are established with the help of Lyapunov functional. The semidiscrete schemes are derived using C0‐piecewise linear finite elements in spatial direction and error estimates are obtained. The semidiscrete problem is then discretized in the temporal direction using backward Euler method and the wellposedness of the completely discrete scheme is discussed. Finally, a priori error estimates are established. While deriving a priori error estimates, Gronwall's lemma is applied and the constants involved in the error bounds do not depend exponentially on \documentclass{article} \usepackage{amsmath, amsthm, amssymb, amsfonts}\pagestyle{empty}\begin{document}$\frac{1}{\gamma}$ \end{document}, where γ is a parameter appeared in the fourth order derivative. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012