×

Two-sided approximations for unilateral variational inequalities by multi-grid methods. (English) Zbl 0635.49006

In this interesting and well written article for the numerical solution of unilateral variational inequalities two iterative schemes are developed which provide approximations from below resp. from above. Both schemes are based on some kind of active set strategy and require the solution of an algebraic system of equations at each iteration step which is done by means of multigrid techniques. Convergence results are established and illustrated by some numerical results for the elastic- plastic torsion problem.
Related results have been obtained in the author’s article in SIAM J. Numer. Anal. 24, 1046-1065 (1987; Zbl 0628.65046).
Reviewer: P.Neitaanmäki

MSC:

49J40 Variational inequalities
49M25 Discrete approximations in optimal control
65K10 Numerical optimization and variational techniques
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
74S30 Other numerical methods in solid mechanics (MSC2010)

Citations:

Zbl 0628.65046
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Glowinski R, Numerical analysis of variational inequalities (1981)
[2] Hackbysch W, Multi-grid methods and applications (1985) · doi:10.1007/978-3-662-02427-0
[3] Hoppe R.H.W, SIAM J. Numer. Anal 24 (5) (1987)
[4] Kinderlehrer D, An introduction to variational inequalities and their applications (1980) · Zbl 0457.35001
[5] Kirsten H, Optimization 16 pp 535– (1985) · doi:10.1080/02331938508843047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.