半线性抛物型积分微分方程的间断时空有限元方法  

THE SPACE-TIME DISCONTINUOUS FINITE ELEMENT METHOD FOR A SEMI-LINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION

作　　者：李宏 王焕清[1,2] 

机构地区：[1]内蒙古大学理工学院数学系 [2]渤海大学数学系,锦州121000

出　　处：《计算数学》2006年第3期293-308,共16页Mathematica Numerica Sinica

基　　金：国家自然科学基金;数学天元基金(A0324652);内蒙古自然科学基金;内蒙古大学博士科研启动项目和513项目资助.

摘　　要：本文讨论了一类半线性抛物型积分微分方程的间断时空有限元方法．利用有限元和有限差分方法相结合的技巧,在时间离散区间内,利用Radau点处Lagrange插值多项式的特性,去掉间断时空有限元的传统证明过程中对时空网格的限制条件,并给出了时间最大模、空间L_2模,即L_∞(L_2)模的误差估计．Adaptive space-time finite element method, continuous in space but discontinuous in time for a semilinear parabolic integro-differential equation is discussed. The approach is based on combination of finite element and finite difference techniques. In the discrete intervals of time, using properties of Lagrange interpolating polynomials at Radau points, eliminate the restriction to space-time meshes of conventional space-time discontinuous Galerkin methods. Error estimate in L∞（L2） norm, that is Maximum-norm in time, L2-norm in space are obtained.

关 键 词：半线性积分微分方程 时空有限元方法 误差估计 

分 类 号：O175.6[理学—数学]