一类四阶抛物方程的混合有限元方法  

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

作　　者：朱维钧[1] 张厚超[1] 

机构地区：[1]平顶山学院数学与信息科学学院,河南平顶山467000

出　　处：《河北师范大学学报（自然科学版）》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)

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.

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 

分 类 号：O242.21[理学—计算数学]