On the numerical solution of involutive ordinary differential systems

Publisher Website
Google Scholar
Abstract
We consider a Galerkin finite element method that uses piecewise bilinears on a modified Shishkin mesh for a model singularly perturbed convection–diffusion problem on the unit square. The method is shown to be convergent, uniformly in the perturbation parameter ε, of order N−1in a global energy norm, provided only that ε ≤ N−1, where O(N2)mesh points are used. Thus on the new mesh the method yields more accurate results than on Shishkin’s original piecewise uniform mesh, where it is convergent of order N−1lnN. Numerical experiments support our theoretical results.

This publication has 5 references indexed in Scilit: