Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D
arXiv:1710.032625 citationsh-index: 24
Originality Incremental advance
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Provides a counterexample for a known theoretical gap in finite element error analysis, confirming the necessity of the logarithmic factor for 3D linear elements.
The authors construct a tetrahedral mesh in 3D for which the logarithmic factor in maximum norm error estimates for linear finite elements cannot be removed, proving that the standard upper bound is sharp.
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.