Centro de Matematica -

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Numerical Approximation Methods for Variational and Quasivariational Inequalities

Elliptic variational inequalities. General approximation results in function spaces. Internal approximations. Penalization of the variational inequality and of the optimization problem. Optimization algorithms. Applications of Semismooth Newton methods to the elliptic case.

Parabolic variational inequalities. Abstract approximation results. Weak and strong solutions. Implicit and explicit discretization schemes. Stability and convergence.

Elliptic quasi-variational inequalities. Iterative methods for the obstacle problem. The concavity and monotonicity approach (robustness of the method). Iterative methods for the general problem and contraction results. Sequential minimization approach and its convergence. Semismooth Newton methods for the elliptic QVI.
Parabolic quasi-variational inequalities. The semigroup approach for the problem. Abstract approximation results. Convergence in semi-discrete schemes. Implicit schemes and application in the "causal" constraint case. Contractive behavior of the solution mapping.

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