Superconvergence analysis of nonconforming FEM for nonlinear time-dependent thermistor problem

摘要

In this paper, we study the superconvergence analysis of nonlinear time-dependent thermistor problem with the well-known nonconforming element, i.e., the extension of the rotated bilinear element (denoted EQ1rot), for the semi-discrete and a linearized backward Euler fully-discrete schemes. The superclose and superconvergent estimates about the related variables in broken H1-norm are derived with the help of the rigorous analysis together with the special properties of this element, mean value technique and interpolated post-processing approach. Finally, a numerical experiment is carried out to confirm the theoretical analysis.