河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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一类四阶抛物方程的混合有限元方法

平顶山学院数学与信息科学学院, 河南平顶山 467000
DOI： 10.13763/j.cnki.jhebnu.nse.2016.03.002

Analysis of a Mixed Finite Element Method for a Fourth-order Parabolic Equation

ZHU Weijun, ZHANG Houchao

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摘要/Abstract

摘要：

利用双二次元对一类四阶抛物方程建立混合有限元格式, 并证明半离散和向后欧拉全离散格式逼近解的存在唯一性. 利用双二次元插值的高精度结果及关于时间变量的导数转移技巧, 在半离散格式和向后欧拉全离散格式下得到了原始变量 u和中间变量v=Δu的H¹模的O(h⁴)阶和O(h⁴+τ)阶的超逼近性质.其中,h,τ分别表示空间剖分参数和时间步长.

Abstract：

A mixed element scheme is established for a fourth-order parabolic equation by applying biquadratic element.The existence and uniqueness of the approximated solutions under semi-discrete scheme and backward Euler fully-discrete scheme are proved.By using high accuracy results for interpolation of biquadratic finite element and derivative transferring technique with respect to the time variable, the super close results with orders O(h⁴) and O(h⁴+τ) of original variable u and intermediate variable v=Δu in H¹ norm are obtained under semi-discrete scheme and backward Euler fully-discrete scheme.Here h and τ are parameter of subdivision in space and time step.

关键词

关键词： 四阶抛物方程 ; 混合元方法 ; 半离散与全离散格式 ; 超逼近

Key words： fourth-order parabolic equation ; mixed finite element method ; semi-discrete and fully-discrete scheme ; superclose

参考文献 13

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