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 is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical space and the hyperbolic part 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 - and -norms for the scalar unknown and a priori error estimates in -norm for its gradient and its flux (the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.