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Licensed Unlicensed Requires Authentication Published by De Gruyter August 21, 2023

Error analysis for a Crouzeix–Raviart approximation of the p-Dirichlet problem

  • Alex Kaltenbach

Abstract

In the present paper, we examine a Crouzeix–Raviart approximation for non-linear partial differential equations having a (p, δ)-structure for some p ∈ (1, ∞) and δ⩾0. We establish a priori error estimates, which are optimal for all p ∈ (1, ∞) and δ⩾0, medius error estimates, i.e., best-approximation results, and a primal-dual a posteriori error estimate, which is both reliable and efficient. The theoretical findings are supported by numerical experiments.

MSC 2010: 49M29; 65N15; 65N50

Acknowledgement

The author is grateful for the stimulating discussions with S. Bartels.

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Received: 2022-10-21
Published Online: 2023-08-21

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