Mixed finite element methods for a fourth order reaction diffusion equation

Authors

  • P. Danumjaya,

    Corresponding author
    1. Department of Mathematics, Birla Institute of Technology and Science - Pilani, Goa Campus, Zuarinagar, Goa 403 726, India
    • Department of Mathematics, Birla Institute of Technology and Science - Pilani, Goa Campus, Zuarinagar, Goa 403 726, India
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  • Amiya K. Pani

    1. Department of Mathematics, Industrial Mathematics Group (IMG), Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
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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 equation image, where γ is a parameter appeared in the fourth order derivative. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012

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