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

[摘要] 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 classicalH(div;Ω)space and the hyperbolic partd(x)(∂u/∂t)+c(x,t)·∇uis 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 inL2- andH1-norms for the scalar unknownuand a priori error estimates in(L2)2-norm for its gradientλand its fluxσ(the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.

[学科分类] 应用数学