EQ 1 rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations |
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Authors: | Yan-min Zhao Fen-ling Wang Dong-yang Shi |
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Affiliation: | 1205. School of Mathematics and Statistics, Xuchang University, Xuchang, 461000, China 2205. Department of Mathematics, Zhengzhou University, Zhengzhou, 450001, China
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Abstract: | EQ 1 rot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h 2) one order higher than its interpolation error O(h), the superclose results of order O(h 2) in broken H 1-norm are obtained. At the same time, the global superconvergence in broken H 1-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h 4) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ 1 rot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature. |
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Keywords: | nonlinear dual phase lagging heat conduction equations EQrot nonconforming finite element superclose and superconvergence extrapolation semi-discrete and fully-discrete schemes |
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