Volume 8, pp. 36-45, 1999.

On a posteriori error estimators in the finite element method on anisotropic meshes

Manfred Dobrowolski, Steffen Gräf, and Christoph Pflaum


On anisotropic finite element meshes, the standard residual based error indicator is derived and it is proved that it is not efficient if the aspect ratio deteriorates. For a nonlocal error indicator it is proved that it is reliable and efficient independent of the aspect ratio. This is also confirmed by some numerical calculations.

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Key words

finite elements, a posteriori estimators, anisotropic meshes.

AMS subject classifications

65N30, 65N15.

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