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

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In this paper, we derive quasi-norm a priori and a posteriori error estimates for the Crouzeix-Raviart type finite element approximation of the p-Laplacian. Sharper a priori upper error bounds are obtained. For instance, for sufficiently regular solutions we prove optimal a priori error bounds on the discretization error in an energy norm when \(1 < p \leq 2\). We also show that the new a posteriori error estimates provide improved upper and lower bounds on the discretization error. For sufficiently regular solutions, the a posteriori error estimates are further shown to be equivalent on the discretization error in a quasi-norm.

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Received January 25, 1999 / Revised version received June 5, 2000 Published online March 20, 2001

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Liu, W., Yan, N. Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of p-Laplacian. Numer. Math. 89, 341–378 (2001). https://doi.org/10.1007/PL00005470

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  • DOI: https://doi.org/10.1007/PL00005470

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