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Mixed finite element methods for a fourth order reaction diffusion equation

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Title Mixed finite element methods for a fourth order reaction diffusion equation
 
Creator DANUMJAYA, P
PANI, AK
 
Subject fourth order reaction diffusion equations
fisher Kolmogorov equation
mixed fem
a prior error estimates
completely discrete scheme
existence and uniqueness of the discrete problem
Lyapunov functional
Gronwall's Lemma
numerical experiment
SPLINE COLLOCATION METHODS
VELOCITY SELECTION
MARGINAL STABILITY
FRONT PROPAGATION
 
Description Mixed 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 ? is a parameter appeared in the fourth order derivative. (c) 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012
 
Publisher WILEY-BLACKWELL
 
Date 2014-10-16T15:10:01Z
2014-10-16T15:10:01Z
2012
 
Type Article
 
Identifier NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 28(4)1227-1251
http://dx.doi.org/10.1002/num.20679
http://dspace.library.iitb.ac.in/jspui/handle/100/15867
 
Language en