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 计算数学 2019, Vol. 41 Issue (2): 191-211    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles 1. 平顶山学院 数学与统计学院, 平顶山 467000;
2. 郑州大学 数学与统计学院, 郑州, 450001
SUPERCONVERGENCE ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC EQUATION
Wang Junjun1, Li Qingfu1, Shi Dongyang2
1. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
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Abstract： An H1-Galerkin mixed finite element method is discussed for nonlinear parabolic equations with the bilinear element and the zero-order Raviart-Thomas element (Q11+Q10×Q01). A linearized second order fully-discrete scheme is proposed. The superclose results with O(h2 + τ2) of original variant u in H1-norm and flux variant p in L2-norm are derived technically. A time semi-discrete equation at the starting point is introduced and the superclose property of ▽·p in L2-norm is reduced. Furthermore, the corresponding global superconvergence results are obtained by the interpolated postprocessing technique. At last, numerical results are presented to illustrate the feasibility of the proposed method (Here, h is the subdivision parameter, and τ, the time step).

 引用本文: . 非线性抛物方程混合有限元方法的高精度分析[J]. 计算数学, 2019, 41(2): 191-211. . SUPERCONVERGENCE ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC EQUATION[J]. Mathematica Numerica Sinica, 2019, 41(2): 191-211.

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