ABSTRACT Superconvergence analysis for a nonlinear parabolic equation is studied with a linearized 2-step backward differential formula (BDF) Galerkin finite element method (FEM). The error between the exact solution and the numerical solution is split into two parts by a time-discrete system. The temporal error estimates in -norm with order and in -norm with order are derived, respectively. The spatial error estimates are deduced unconditionally and the results help to bound the numerical solution in -norm. By some new way, the unconditional superclose property of in -norm with order is obtained. Two numerical examples show the validity of the theoretical analysis. Here, h is the subdivision parameter, and τ, time step size.

中文翻译：

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BDF有限元法对非线性抛物线方程的超收敛分析

摘要 非线性抛物线方程的超收敛分析用线性化的 2 步后向微分公式 (BDF) 伽辽金有限元法 (FEM) 进行了研究。精确解与数值解之间的误差被时间离散系统分成两部分。分别推导出-norm with order 和in-norm with order 中的时间误差估计。空间误差估计是无条件推导出来的，结果有助于在 -norm 中限制数值解。通过某种新的方式，得到了 in-norm with order 的无条件超接近性质。两个数值例子表明了理论分析的有效性。其中，h 是细分参数，τ 是时间步长。