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Mathematics of Computation

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Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D

Author: Natalia Kopteva
Journal: Math. Comp. 88 (2019), 1527-1532
MSC (2010): Primary 65N15, 65N30; Secondary 65N06
Published electronically: September 28, 2018
MathSciNet review: 3925475
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Abstract: For linear finite element discretizations of the Laplace equation in three dimensions, we give an example of a tetrahedral mesh in the cubic domain for which the logarithmic factor cannot be removed from the standard upper bounds on the error in the maximum norm.

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Additional Information

Natalia Kopteva
Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

Keywords: Linear finite elements, maximum norm error estimate, logarithmic factor
Received by editor(s): October 9, 2017
Received by editor(s) in revised form: January 17, 2018, and April 16, 2018
Published electronically: September 28, 2018
Article copyright: © Copyright 2018 American Mathematical Society