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2013 A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems
Yang Liu, Hong Li, Wei Gao, Siriguleng He, Zhichao Fang
J. Appl. Math. 2013: 1-11 (2013). DOI: 10.1155/2013/683205


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.


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Yang Liu. Hong Li. Wei Gao. Siriguleng He. Zhichao Fang. "A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems." J. Appl. Math. 2013 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.65197
MathSciNet: MR3039735
Digital Object Identifier: 10.1155/2013/683205

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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