The splitting mixed element method for parabolic equation and its application in chemotaxis model
| Autor: | Jiansong Zhang, Yuezhi Zhang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Variable coefficient
Applied Mathematics Mathematical analysis Finite difference 010103 numerical & computational mathematics Positive-definite matrix 01 natural sciences 010101 applied mathematics Computational Mathematics Mixed systems Scheme (mathematics) Convergence (routing) Parabolic problem 0101 mathematics Element (category theory) Mathematics |
| Zdroj: | Applied Mathematics and Computation. 313:287-300 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2017.06.011 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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