Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains

Nobito Yamamoto; Mitsuhiro T. Nakao

doi:10.1007/BF01385765

Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains

Nobito Yamamoto^*, Mitsuhiro T. Nakao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

In this paper, methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied. In order to verify solutions using computer, it is necessary to determine some constants which appear in a priori error estimations. We propose some methods for determination of these constants. In numerical examples, calculating these constants for an L-shaped domain, we verify the solution of a nonlinear elliptic equation.

Original language	English
Pages (from-to)	503-521
Number of pages	19
Journal	Numerische Mathematik
Volume	65
Issue number	1
DOIs	https://doi.org/10.1007/BF01385765
Publication status	Published - 1993 Dec
Externally published	Yes

Keywords

Mathematics Subject Classification (1991): 65N15, 65N30

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics
Mathematics(all)

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10.1007/BF01385765

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abstract = "In this paper, methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied. In order to verify solutions using computer, it is necessary to determine some constants which appear in a priori error estimations. We propose some methods for determination of these constants. In numerical examples, calculating these constants for an L-shaped domain, we verify the solution of a nonlinear elliptic equation.",

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AU - Nakao, Mitsuhiro T.

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AB - In this paper, methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied. In order to verify solutions using computer, it is necessary to determine some constants which appear in a priori error estimations. We propose some methods for determination of these constants. In numerical examples, calculating these constants for an L-shaped domain, we verify the solution of a nonlinear elliptic equation.

KW - Mathematics Subject Classification (1991): 65N15, 65N30

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ER -

Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains

Abstract

Keywords

ASJC Scopus subject areas

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