王俊俊¹, 李庆富¹, 石东洋²

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

收稿日期:2017-11-03出版日期:2019-06-15发布日期:2019-05-18


基金资助:国家自然科学基金（11271340），平顶山学院博士启动基金（PXY-BSQD-2019001），平顶山学院培育基金（PXY-PYJJ-2019006）.

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

Received:2017-11-03Online:2019-06-15Published:2019-05-18







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采用双线性元及零阶Raviart-Thomas元（Q₁₁+Q₁₀×Q₀₁）对非线性抛物方程讨论了一种H¹-Galerkin混合有限元方法.提出一个线性化的二阶格式，利用数学归纳法有技巧的导出了原始变量u在H¹（Ω）模意义下及流量p=▽u在L²（Ω）模意义下的O（h²+τ²）阶超逼近性质.引入一个有关初始点的时间离散方程，并利用其得到了▽ ·在L²（Ω）模意义下的O（h²+τ²）阶的超逼近结果.同时利用插值后处理技巧得到整体超收敛.最后，数值算例结果验证了理论分析（其中，h是剖分参数，τ是时间步长）.
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