Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem

✍ Scribed by G. Beckett; J.A. Mackenzie

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 206 KB
• Volume: 35
• Category: Article
• ISSN: 0168-9274
• DOI: 10.1016/s0168-9274(99)00065-3

✦ Synopsis

We derive ε-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, ε is the small parameter multiplying the highest derivative term. The grid is suggested by the equidistribution of a positive monitor function which is a linear combination of a constant floor and a power of the second derivative of the solution. Our analysis shows how the floor should be chosen to ensure ε-uniform convergence and indicates the convergence behaviour for such grids. Numerical results are presented which confirm the ε-uniform convergence rates.