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摘要
A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term del . (a(x,t)del u) is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H(div; Omega) space and the hyperbolic part d(x)(partial derivative u/partial derivative t) + c(x,t) . del 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 L-2- and H-1-norms for the scalar unknown u and a priori error estimates in (L-2)(2)-norm for its gradient lambda and its flux sigma (the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.
- 出版日期2013
- 单位内蒙古大学
