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Maximum Norm Estimates for Energy-Corrected Finite Element Method

  • Piotr SwierczynskiEmail author
  • Barbara Wohlmuth
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

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 L2 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 L2-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.

Notes

Acknowledgements

We gratefully acknowledge the support of the German Research Foundation (DFG) through the grant WO 671/11-1 and, together with the Austrian Science Fund, through the IGDK1754 Training Group. We would also like to thank Dr Johannes Pfefferer for many fruitful and helpful discussions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for Numerical MathematicsTechnical University of MunichMünchenGermany

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