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Error analysis for a Crouzeix-Raviart approximation of the obstacle problem (2302.01646v2)
Published 3 Feb 2023 in math.NA and cs.NA
Abstract: 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. Numerical experiments are carried out to support the theoretical findings.