Some remarks on the optimal L2 error estimates for the finite element method on the L-shaped domain

Takehiko Kinoshita, Mitsuhiro T. Nakao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the a priori L2 error analysis of the finite element method (FEM), the Aubin-Nitsche trick is often used. Usually, the convergence order of the L2 error estimates by the Aubin-Nitsche trick is one order higher than the H0 1 error estimates. As is well known, the convergence order obtained by this technique depends on the shape of the domain because it is dependent on the regularity of solutions for the associated dual problem on the same domain. In this paper, we introduce a technique for getting the optimal order L2 error estimates on the L-shaped domain without Aubin-Nitsche trick. From the numerical evidence based on the guaranteed computations, we could still expect that such a domain dependency is not essential.

Original languageEnglish
Title of host publicationProceedings of the 2013 10th International Conference on Information Technology
Subtitle of host publicationNew Generations, ITNG 2013
Pages173-178
Number of pages6
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event2013 10th International Conference on Information Technology: New Generations, ITNG 2013 - Las Vegas, NV, United States
Duration: 2013 Apr 152013 Apr 17

Other

Other2013 10th International Conference on Information Technology: New Generations, ITNG 2013
CountryUnited States
CityLas Vegas, NV
Period13/4/1513/4/17

Fingerprint

Finite element method
Error analysis

Keywords

  • computational a priori estimate
  • finite element method
  • L error estimates
  • non-convex domain
  • Poisson equation

ASJC Scopus subject areas

  • Information Systems

Cite this

Kinoshita, T., & Nakao, M. T. (2013). Some remarks on the optimal L2 error estimates for the finite element method on the L-shaped domain. In Proceedings of the 2013 10th International Conference on Information Technology: New Generations, ITNG 2013 (pp. 173-178). [6614306] https://doi.org/10.1109/ITNG.2013.30

Some remarks on the optimal L2 error estimates for the finite element method on the L-shaped domain. / Kinoshita, Takehiko; Nakao, Mitsuhiro T.

Proceedings of the 2013 10th International Conference on Information Technology: New Generations, ITNG 2013. 2013. p. 173-178 6614306.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kinoshita, T & Nakao, MT 2013, Some remarks on the optimal L2 error estimates for the finite element method on the L-shaped domain. in Proceedings of the 2013 10th International Conference on Information Technology: New Generations, ITNG 2013., 6614306, pp. 173-178, 2013 10th International Conference on Information Technology: New Generations, ITNG 2013, Las Vegas, NV, United States, 13/4/15. https://doi.org/10.1109/ITNG.2013.30
Kinoshita T, Nakao MT. Some remarks on the optimal L2 error estimates for the finite element method on the L-shaped domain. In Proceedings of the 2013 10th International Conference on Information Technology: New Generations, ITNG 2013. 2013. p. 173-178. 6614306 https://doi.org/10.1109/ITNG.2013.30
Kinoshita, Takehiko ; Nakao, Mitsuhiro T. / Some remarks on the optimal L2 error estimates for the finite element method on the L-shaped domain. Proceedings of the 2013 10th International Conference on Information Technology: New Generations, ITNG 2013. 2013. pp. 173-178
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