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Multilevel projection algorithm for solving obstacle problems

โœ Scribed by Yongmin Zhang

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
503 KB
Volume
41
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

Obstacle problems are nonlinear free boundary problems and the computation of ap* proximate solutions can be difficult and expensive. Little work has been done on effective numerical methods of such problems. This paper addresses some aspects of this issue. Discretizing the problem in a continuous piecewise linear finite element space gives a quadratic programming problem with inequality constraints. A new method, called the multilevel projection (MP) method, is established in this paper. The MP algorithm extends the multigrid method for linear equations to nonlinear obstacle problems. The convergence theorems of this method are also proved. A numerical example presented shows our error estimate is sharp and the MP algorithm is robust.

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