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.
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（h^4）and O（h^4＋τ）of original variable uand intermediate variable v=Δuin H^1 norm are obtained under semi-discrete scheme and backward Euler fully-discrete scheme.Here h andτare parameter of subdivision in space and time step.
出处
《河北师范大学学报（自然科学版）》
CAS
2016年第3期189-194,共6页
Journal of Hebei Normal University：Natural Science
基金
国家自然科学基金(11271340)
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
fourth-order parabolic equation
mixed finite element method
semi-discrete and fully-discrete scheme
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