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Mixed finite element methods for a fourth order reaction diffusion equation
Article first published online: 15 MAY 2011
DOI: 10.1002/num.20679
Copyright © 2010 Wiley Periodicals, Inc.
Issue
Numerical Methods for Partial Differential Equations
Volume 28, Issue 4, pages 1227–1251, July 2012
Additional Information
How to Cite
Danumjaya, P. and Pani, A. K. (2012), Mixed finite element methods for a fourth order reaction diffusion equation. Numer. Methods Partial Differential Eq., 28: 1227–1251. doi: 10.1002/num.20679
Publication History
- Issue published online: 20 APR 2012
- Article first published online: 15 MAY 2011
- Manuscript Accepted: 28 APR 2010
- Manuscript Received: 14 SEP 2009
Funded by
- Department of Science and Technology, Government of India. Grant Number: 08DST012
- Abstract
- Article
- References
- Cited By
Keywords:
- 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
Abstract
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 
, where γ is a parameter appeared in the fourth order derivative. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012