A discontinuous Galerkin least-squares finite element method for solving Fisher's equation

Pages: 489 - 497, Issue special, November 2013

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Runchang Lin - Department of Engineering, Mathematics, and Physics, Texas A&M International University, Laredo, TX 78041, United States (email)
Huiqing Zhu - Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406, United States (email)

Abstract: In the present study, a discontinuous Galerkin least-squares finite element algorithm is developed to solve Fisher's equation. The present method is effective and can be successfully applied to problems with strong reaction, to which obtaining stable and accurate numerical traveling wave solutions is challenging. Numerical results are given to demonstrate the convergence rates of the method and the performance of the algorithm in long-time integrations.

Keywords:  Fisher's equation, least-squares finite element method, discontinuous Galerkin method.
Mathematics Subject Classification:  Primary: 65M60, 65M12.

Received: September 2012;      Revised: January 2013;      Published: November 2013.