Finite Element Approximation of Nonlinear Variational Inequalities Arising in Porous Media
In this paper, we are concerned with the approximate solution by the finite element technique of a fairly large class of nonlinear variational inequalities encountered in the study of a model of groudwater flow in a partially saturated porous media. Using the smooth perturbation (regularization) of variational inequalities and piece-wise linear conforming elements, we show that the error for the approximate solution of nonlinear variational inequalities is of order h in the energy norm. In fact, our estimates improve all of the previous known results for elliptic variational inequalities. We also discuss special cases, which can be obtained from our general result.
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