Numerical approximation of a unilateral obstacle problem. (English) Zbl 1251.47054
The authors consider a unilateral obstacle problem in the variational inequality form. Then they utilize its variational inclusion formulation proposed in [A. Addou and E. B. Mermri, “Sur une méthode de résolution d’un problème d’obstacle”, Math-Rech. Appl. 2, 59–69 (2000; MR1836181)]. It is approximated by using finite element and projection methods. A strong convergence result is established. The results of the solution of a one-dimensional obstacle problem are also given.
Reviewer: Igor V. Konnov (Kazan)
MSC:
| 47J22 | Variational and other types of inclusions |
| 47J25 | Iterative procedures involving nonlinear operators |
| 49M25 | Discrete approximations in optimal control |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
obstacle problem; variational inequality; variational inclusion; finite element method; convergenceReferences:
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