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Solving obstacle problems with guaranteed accuracy

✍ Scribed by Cheon Seoung Ryoo

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 802 KB
Volume: 45
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(03)00043-9

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✦ Synopsis

In this paper, we consider a numerical technique which enables us to verify the existence of solutions for some simple obstacle problems. Using the finite element approximation and constructive error estimates, we construct, on a computer, a set of solutions which satisfies the hypothesis of the Schauder fixed-point theorem for a compact map on a certain Sobolev space. We describe the numerical verification algorithm for solving a two-dimensional obstacle problems and report some numerical results.

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