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 ac...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).展开更多
文摘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).
