A novel characteristic expanded mixed method for reaction-convection- diffusion problems

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 (d i v; 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 l 2 - and h 1 -norms for the scalar unknown u and a priori error estimates in (l 2) 2 -norm for its gradient and its flux σ (the coefficients times the negative gradient) are derived. finally,a numerical example is provided to verify our theoretical results. © 2013 yang liu et al.