Local A Posteriori Estimates on a Nonconvex Polygonal Domain
SIAM Journal on Numerical Analysis
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In this paper we define an a posteriori error estimator for finite element approximations of 3-d elliptic problems. We prove that the estimator is equivalent, up to logarithmic factors of the meshsize, to the maximum norm of the error. The results are valid for an arbitrary polyhedral domain and rather general meshes. We also obtain analogous results for the nonconforming method of Crouzeix--Raviart. Finally, we present some numerical results comparing adaptive procedures based on controlling the error in different norms.