On The Finite Element Approximation of Quasi variational Inequalities with Nonlinear Source.

Variational inequalities and quasivariational inequalities model important problems arising in different disciplines of science and engineering such as, contact mechanics, obstacle problem, stochastic control problems, inventory, games theory, cash management, superconductivity, semiconductor devices, option pricing, flow through porous media, dam problem, sand pile model, elastoplasticity, and rigid punch problem. Techniques, methods and simulation of variational inequalities have provided solution of many highly nonlinear problems earlier thought to be inaccessible. In this project we will study the standard finite element approximation in the L- norm of the following class of quasi variational inequalities (qvi): Find uandisin;such that , +, + Here andOmega; is a bounded domain of RN, Nandge;1, with smooth boundary, a(u,v) is coercive elliptic bilinear form, f and andpsi; are regular funtions and andphi; a nonlinear continuous operator from L(andOmega;) into itself. The class of QVIs under consideration includes at least the following two important problems: variational inequalities of obstacle type problems and quasi variational inequalities arising in impulse control and filtration in porous media. In this project, we will be interested in deriving finite element error estimates for the above problem, under milder assumptions on the nonlinearity f(.) than those existing in the literature