Unconditional Superconvergence Analysis for Nonlinear Parabolic Equation with EQ1rot\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \beg

Nonlinear parabolic equation is studied with a linearized Galerkin finite element method. First of all, a time-discrete system is established to split the error into two parts which are called the temporal error and the spatial error, respectively. On one hand, a rigorous analysis for the regularity of the time-discrete system is presented based on the proof of the temporal error skillfully. On the other hand, the spatial error is derived $$\tau $$τ-independently with the above achievements. Then, the superclose result of order $$O(h^2+\tau ^2)$$O(h2+τ2) in broken $$H^1$$H1-norm is deduced without any restriction of $$\tau $$τ. The two typical characters of the $${\textit{EQ}}_1^{rot}$$EQ1rot nonconforming FE (see Lemma 1 below) play an important role in the procedure of proof. At last, numerical results are provided in the last section to confirm the theoretical analysis. Here, h is the subdivision parameter, and $$\tau $$τ, the time step.