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

Takehiko Kinoshita; Mitsuhiro T. Nakao

doi:10.1109/ITNG.2013.30

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 proceeding › Conference 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 language	English
Title of host publication	Proceedings of the 2013 10th International Conference on Information Technology
Subtitle of host publication	New Generations, ITNG 2013
Pages	173-178
Number of pages	6
DOIs	https://doi.org/10.1109/ITNG.2013.30
Publication status	Published - 2013
Externally published	Yes
Event	2013 10th International Conference on Information Technology: New Generations, ITNG 2013 - Las Vegas, NV, United States Duration: 2013 Apr 15 → 2013 Apr 17

Other

Other	2013 10th International Conference on Information Technology: New Generations, ITNG 2013
Country/Territory	United States
City	Las Vegas, NV
Period	13/4/15 → 13/4/17

Keywords

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

ASJC Scopus subject areas

Information Systems

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10.1109/ITNG.2013.30

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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

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

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.",

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language = "English",

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note = "2013 10th International Conference on Information Technology: New Generations, ITNG 2013 ; Conference date: 15-04-2013 Through 17-04-2013",

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T1 - Some remarks on the optimal L2 error estimates for the finite element method on the L-shaped domain

AU - Kinoshita, Takehiko

AU - Nakao, Mitsuhiro T.

PY - 2013

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N2 - 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.

AB - 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.

KW - computational a priori estimate

KW - finite element method

KW - L error estimates

KW - non-convex domain

KW - Poisson equation

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DO - 10.1109/ITNG.2013.30

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BT - Proceedings of the 2013 10th International Conference on Information Technology

T2 - 2013 10th International Conference on Information Technology: New Generations, ITNG 2013

Y2 - 15 April 2013 through 17 April 2013

ER -

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

Abstract

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Keywords

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