伪双曲型积分-微分方程的H^1-Galerkin混合元法误差估计  

ERROR ESTIMATES OF H^1-GALERKIN MIXED FINITE ELEMENT METHODS FOR PSEUDO-HYPERBOLIC PARTIAL INTEGRO-DIFFERENTIAL EQUATION

作　　者：刘洋[1] 李宏 何斯日古楞 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《高等学校计算数学学报》2010年第1期1-20,共20页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目资助(10601022);内蒙古自然科学基金资助(200607010106);内蒙古大学青年科学基金项目(ND0702);内蒙古大学513项目资助

摘　　要：1引言考虑如下一类具有Lipschitz连续边界（?）Ω的凸有界区域Ω上的伪双曲型积分微分方程其中Ω（?）Rd,（d=1,2,3）J=(0,T],对于固定的T,0<T<∞,函数0<a0≤a（x。H1-Galerkin mixed finite element methods are discussed for a class of second order pseudo-hyperbolic partial integro-differential equation. Two fi- nite element methods are analysed, and the existence and uniqueness of solutions in continuous problems and discrete ones are proved respectively. Optimal er- for estimates are derived for problems in one space dimension. An extension of Hl-Galerkin mixed finite element method to problems with two and three space variables is also discussed and at the same time, error estimates are given and it is showed that the H1- Galerkin mixed finite element approximations do not require the LBB consistency condition. Finally, the feasibility of numerical methods are verified by the numerical examples.

关 键 词：pseudo-hyperbolic partial integro-differential equation H^1-Galerkin mixed finite element methods existence and UNIQUENESS error estimates 

分 类 号：O242.21[理学—计算数学]