带广义边界条件的四阶抛物型方程的混合间断时空有限元法  

THE MIXED DISCONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR THE FOURTH ORDER LINEAR PARABOLIC EQUATION WITH GENERALIZED BOUNDARY CONDITION

作　　者：何斯日古楞 李宏 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《计算数学》2009年第2期167-178,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金10601022;内蒙古自然科学基金200607010106;内蒙古大学513项目资助.

摘　　要：构造具有广义边界条件的四阶线性抛物型方程的混合间断时空有限元格式,利用混合有限元方法将高阶方程降阶,利用空间连续而时间允许间断的时空有限元方法离散方程,证明了离散解的存在唯一性,稳定性和收敛性,并给出数值算例验证了方法的有效性.The mixed discontinuous space-time finite element method for the fourth order linear parabolic equation with generalized boundary conditions are constructed. The order of the equations is lowered by mixed finite element method, and the lowered second order equation is discretizd by the space-time finite element method which is continuous in space but discontinuous in time. The stability, uniqueness and existence, and error estimates of the approximate solution are proved.And the numerical simulations are given to illustrate the efficiency of the method.

关 键 词：四阶线性抛物型方程 广义边界条件 混合有限元法 时间间断时空有限元法 

分 类 号：O241.82[理学—计算数学]