FINITE ELEMENT ANALYSIS OF A LOCAL EXPONENTIALLYFITTED SCHEME FOR TIME-DEPENDENTCONVECTION-DIFFUSION PROBLEMS  

作　　者：Yue, XY Jiang, LS Shih, TM 

机构地区：[1]Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China [2]Tongji Univ, Inst Math, Shanghai 200092, Peoples R China [3]Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong

出　　处：《Journal of Computational Mathematics》1999年第3期225-232,共8页计算数学（英文）

摘　　要：In [16], Stynes and O' Riordan(91) introduced a local exponentially fitted finite element (FE) scheme for a singularly perturbed two-point boundary value problem without turning-point. An E-uniform h(1/2)-order accuracy was obtain for the epsilon-weighted energy norm. And this uniform order is known as an optimal one for global exponentially fitted FE schemes (see [6, 7, 12]). In present paper, this scheme is used to a parabolic singularly perturbed problem. After some subtle analysis, a uniformly in epsilon convergent order h\ln h\(1/2) + tau is achieved (h is the space step and tau is the time step), which sharpens the results in present literature. Furthermore, it implies that the accuracy order in [16] is actuallay h\ln h\(1/2) rather than h(1/2).In [16], Stynes and O' Riordan(91) introduced a local exponentially fitted finite element (FE) scheme for a singularly perturbed two-point boundary value problem without turning-point. An E-uniform h(1/2)-order accuracy was obtain for the epsilon-weighted energy norm. And this uniform order is known as an optimal one for global exponentially fitted FE schemes (see [6, 7, 12]). In present paper, this scheme is used to a parabolic singularly perturbed problem. After some subtle analysis, a uniformly in epsilon convergent order h\ln h\(1/2) + tau is achieved (h is the space step and tau is the time step), which sharpens the results in present literature. Furthermore, it implies that the accuracy order in [16] is actuallay h\ln h\(1/2) rather than h(1/2).

关 键 词：singularly perturbed exponentially fitted uniformly in epsilon convergent Petrov-Galerkin finite element method 

分 类 号：O241[理学—计算数学]