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

Natalia Kopteva

doi:10.1090/mcom/3384

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

Natalia Kopteva

Department of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1527-1532
Number of pages	6
Journal	Mathematics of Computation
Volume	88
Issue number	318
DOIs	https://doi.org/10.1090/mcom/3384
Publication status	Published - 1 Sep 2018

Keywords

Linear finite elements
Logarithmic factor
Maximum norm error estimate

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10.1090/mcom/3384

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title = "Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D",

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.",

keywords = "Linear finite elements, Logarithmic factor, Maximum norm error estimate",

author = "Natalia Kopteva",

note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

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doi = "10.1090/mcom/3384",

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KW - Linear finite elements

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KW - Maximum norm error estimate

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

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