Abstract
We propose and analyse a nonconforming finite element method for numerical approximation of the solution of a parabolic variational inequality associated with general obstacle. In this article, we carry out the error analysis for both the semi-discrete and fully-discrete schemes. We use the backward Euler method for time discretization and the lowest order Crouzeix-Raviart nonconforming finite element method for space discretization. The main motivation for the space discretization with Crouzeix-Raviart nonconforming finite element method to the parabolic obstacle problem is that it gives a natural -stable interpolation which is commutative with the time derivative. By taking full advantage of this commutative property together with -stability of interpolation, we derive an error estimate of the order for semi-discrete scheme, and error estimate of order for fully-discrete scheme in a certain norm defined precisely in the article.
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