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2019 | OriginalPaper | Chapter

Maximum Norm Estimates for Energy-Corrected Finite Element Method

Authors : Piotr Swierczynski, Barbara Wohlmuth

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2017

Publisher: Springer International Publishing

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Abstract

Nonsmoothness of the boundary of polygonal domains limits the regularity of the solutions of elliptic problems. This leads to the presence of the so-called pollution effect in the finite element approximation, which results in a reduced convergence order of the scheme measured in the L 2 and L ∞-norms, compared to the best-approximation order. We show that the energy-correction method, which is known to eliminate the pollution effect in the L 2-norm, yields the same convergence order of the finite element error as the best approximation also in the L ∞-norm. We confirm the theoretical results with numerical experiments.

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previous chapter Exponential Scaling and the Time Growth of the Error of DG for Advection-Reaction Problems
next chapter Digital Operators, Discrete Equations and Error Estimates
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Metadata
Title
Maximum Norm Estimates for Energy-Corrected Finite Element Method
Authors
Piotr Swierczynski
Barbara Wohlmuth
Copyright Year
2019
Book
Numerical Mathematics and Advanced Applications ENUMATH 2017

Print ISBN: 978-3-319-96414-0

Electronic ISBN: 978-3-319-96415-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-96415-7_92

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