Global pointwise error estimates for uniformly convergent finite element methods for the elliptic boundary layer problem

✍ Scribed by J. Li

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 416 KB
• Volume: 36
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(98)00109-6

✦ Synopsis

This paper continues our discussion for the anisotropic model problem-(e o--~x-{-o--~ )

• a(z, y)u = f(x, y) in [1]. There we constructed a bilinear finite element method on a Shishkin type mesh. The method was shown to be convergent, independent of the small parameter e, in the order of N -2 In 2 N in the L2-norm, where N 2 is the total number of mesh points. In this paper, the method is shown to be convergent, independent of e, in the order of N -2 In 3 N in the L°°-norm in the whole computational domain, which explains the uniform convergence phenomena we found in the numerical results in [1]. Another numerical experiment is presented here, which confirms our theoretical analysis. Published by Elsevier Science Ltd. Keywords--Finite element methods, Singularly perturbed problems, Elliptic partial differential equations, Pointwise error estimates.