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

Anovel characteristic expanded mixed finite elementmethod 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 H(div; o) 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 L²- and H¹-norms for the scalar unknown and a priori error estimates in (L²)²-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. [ABSTRACT FROM AUTHOR]