Unconditional Superconvergence Analysis for Nonlinear Parabolic Equation with EQ(1)(rot) Nonconforming Finite Element

摘要

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 -independently with the above achievements. Then, the superclose result of order in broken -norm is deduced without any restriction of . The two typical characters of the 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 , the time step.