Remainder estimates in Taylor's theorem
American Mathematical Monthly
Pointwise a posteriori error estimates for elliptic problems on highly graded meshes
Mathematics of Computation
Interior maximum-norm estimates for finite element methods, part II
Mathematics of Computation
Maximum Norm Error Estimators for Three-Dimensional Elliptic Problems
SIAM Journal on Numerical Analysis
Pointwise Error Estimates for Differences in Piecewise Linear Finite Element Approximations
SIAM Journal on Numerical Analysis
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A class of a posteriori estimators is studied for the error in the maximum norm of the gradient on single elements when the finite element method is used to approximate solutions of second order elliptic problems on a nonconvex polygonal domain. The results are extensions of previous results for smooth domains [W. Hoffmann et al., Math. Comp., 70 (2001), pp. 897-909; A. H. Schatz and L. B. Wahlbin, Math. Comp., 73 (2004), pp. 517-523].