Error analysis for a Crouzeix-Raviart approximation of the obstacle problem

02/03/2023

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by   Sören Bartels, et al.

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In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements of a triangulation. We establish a priori error estimates imposing natural regularity assumptions, which are optimal, and the reliability and efficiency of a primal-dual type a posteriori error estimator for general obstacles and involving data oscillation terms stemming only from the right-hand side. The theoretical findings are supported by numerical experiments.