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 τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}-independently with the above achievements. Then, the superclose result of order O(h2+τ2)\documentclass[12pt]{minimal}
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\begin{document}$$O(h^2+\tau ^2)$$\end{document} in broken H1\documentclass[12pt]{minimal}
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\begin{document}$$H^1$$\end{document}-norm is deduced without any restriction of τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}. The two typical characters of the EQ1rot\documentclass[12pt]{minimal}
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\begin{document}$${\textit{EQ}}_1^{rot}$$\end{document} 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 τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}, the time step.
