Quasi-norm a priori and a posteriori error estimates for the nonconformingapproximation of p-Laplacian

In this paper., we derive quasi-norm a priori and a posteriori error estima tes for the Crouzeix-Raviart type finite element approximation of the p-Lap lacian. Sharper a priori upper error bounds are obtained. For instance, for sufficiently regular solutions we prove optimal a priori error bounds on t he discretization error in an energy norm when 1 < p less than or equal to 2. We also show that the new a posteriori error estimates provide improved upper and lower bounds on the discretization error. For sufficiently regula r solutions, the a posteriori error estimates are further shown to be equiv alent on the discretization error in a quasi-norm.