Abstract

In this paper, a backward-Euler mixed finite element (MFE) approximation scheme is presented for the non-stationary conduction–convection problem, in which the constrained nonconforming rotated (CNR) Q1 element is used to approximate the velocity u, the temperature T and the Q0 element to the pressure p. Based on the characters of these elements and some special skills, i.e., mean-value skill and a new transforming skill with respect to τ, the superclose results of order O(h2+τ) for u,T in the broken H1-norm and p in L2-norm are deduced, respectively. Here, h is the subdivision parameter and τ, the time step. Furthermore, the global superconvergent results are obtained through the interpolation postprocessing technique. Finally, numerical results are provided to confirm the theoretical analysis.

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