TY - JOUR

T1 - Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part 1

T2 - A smooth problem and globally quasi-uniform meshes

AU - Hoffmann, W.

AU - Schatz, A. H.

AU - Wahlbin, L. B.

AU - Wittum, Gabriel

PY - 2001/7/1

Y1 - 2001/7/1

N2 - 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. The meshes are unstructured and, in particular, it is not assumed that there are any known superconvergent points. The estimators are based on averaging operators which are approximate gradients, "recovered gradients", which are then compared to the actual gradient of the approximation on each element. Conditions are given under which they are asympotically exact or equivalent estimators on each single element of the underlying meshes. Asymptotic exactness is accomplished by letting the approximate gradient operator average over domains that are large, in a controlled fashion to be detailed below, compared to the size of the elements.

AB - 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. The meshes are unstructured and, in particular, it is not assumed that there are any known superconvergent points. The estimators are based on averaging operators which are approximate gradients, "recovered gradients", which are then compared to the actual gradient of the approximation on each element. Conditions are given under which they are asympotically exact or equivalent estimators on each single element of the underlying meshes. Asymptotic exactness is accomplished by letting the approximate gradient operator average over domains that are large, in a controlled fashion to be detailed below, compared to the size of the elements.

UR - http://www.scopus.com/inward/record.url?scp=0039254111&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-01-01286-8

DO - 10.1090/S0025-5718-01-01286-8

M3 - Article

AN - SCOPUS:0039254111

SN - 0025-5718

VL - 70

SP - 897

EP - 909

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 235

ER -