A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion problem. (English) Zbl 0625.65073
A Galerkin finite element method with exponential test functions is applied to a selfadjoint singularly perturbed two-point boundary value problem. By introducing a discretized Green’s function the nodal errors are given explicitly in integral form. The generated scheme is shown to be uniformly second-order accurate. Some numerical results illustrating the difference between the exact solution and its finite element approximation are presented.
Reviewer: C.-I.Gheorghiu
MSC:
65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
34B05 | Linear boundary value problems for ordinary differential equations |
34E15 | Singular perturbations for ordinary differential equations |