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(div; 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 L2‐ and H1‐norms for the scalar unknown u and a priori error estimates in (L2) 2‐norm for its gradient λ and its flux σ (the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.