The splitting mixed element method for parabolic equation and its application in chemotaxis model

Yuezhi Zhang and Jiansong Zhang

Applied Mathematics and Computation, 2017, vol. 313, issue C, 287-300

Abstract: In this article, we first revisit the splitting positive definite mixed element method for reaction-diffusion equation, in which the mixed system is symmetric positive definite. And then we apply this technique to the variable coefficient parabolic equation and give the corresponding fully-discrete scheme with second-order central difference formula in time. We study the convergence of the semi-discrete and fully-discrete scheme and derive the error estimates. Finally, we extend this method to chemotaxis model and give the corresponding numerical results, which suggests that it has the ability to recover blowing-up solutions.

Keywords: Parabolic problem; Splitting system; Mixed finite element; Convergence analysis; Chemotaxis model (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:313:y:2017:i:c:p:287-300

DOI: 10.1016/j.amc.2017.06.011

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