Journal of Applied Mathematics

A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems

Yang Liu, Hong Li, Wei Gao, Siriguleng He, and Zhichao Fang

Full-text: Open access

Abstract

A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ·(a(x,t)u) is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H(div;Ω) space and the hyperbolic part d(x)(u/t)+c(x,t)·u is handled by the characteristic method. For a priori error estimates, some important lemmas based on the novel expanded mixed projection are introduced. The fully discrete error estimates based on backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L2- and H1-norms for the scalar unknown u and a priori error estimates in (L2)2-norm for its gradient λ and its flux σ (the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 683205, 11 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807924

Digital Object Identifier
doi:10.1155/2013/683205

Mathematical Reviews number (MathSciNet)
MR3039735

Zentralblatt MATH identifier
1266.65197

Citation

Liu, Yang; Li, Hong; Gao, Wei; He, Siriguleng; Fang, Zhichao. A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems. J. Appl. Math. 2013 (2013), Article ID 683205, 11 pages. doi:10.1155/2013/683205. https://projecteuclid.org/euclid.jam/1394807924


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