Introduction 23 1. Abstract minimization problems, variational inequalities and the Lax-
Milgram lemma 24 2. The Sobolev spaces H (Q2) and Green's formulae 30 3. Examples of …

In both engineering and physics literature we find many problems solved by intuitive, ad hoc
methods, regardless of the fact that the possibility exists of formulating and solving these …

In accordance with the developments in computation, theoretical studies on numerical
schemes are now fruitful and highly needed. In 1991 an article on the finite element method …

We are interested in the approximation in the L∞-norm of variational inequalities with non-
linear operators and somewhat irregular obstacles. We show that the order of convergence …

This paper is concerned with error estimates for the piecewise linear finite element
approximation of the two-dimensional scalar Signorini problem on a convex polygonal …

In this paper, we present an alternative approach to a priori L^ ∞ L∞-error estimates for the
piecewise linear finite element approximation of the classical obstacle problem. Our …

Zusammenfassung Das Thema dieser Arbeit ist die Bestimmung und die Charakterisierung
verallgemeinerter Ableitungen für Lösungsoperatoren von Hindernisproblemen. Das …

We study parallel algorithms for certain classes of parabolic quasi-variational inequalities
proposed by Lions in 1999, and examine the possibility of applying such algorithms to quasi …

A new monotonicity principle and an L1-stability theorem are established for a discrete
obstacle problem which is de ned by a piecewise linear nite element discretization of a …

Stochastic control problems with ergodic type payoff may be solved by considering the
solution of variational inequalities (VIs) with Neumann boundary conditions, where the …