Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element

Nobito Yamamoto; Mitsuhiro T. Nakao

doi:10.1016/0377-0427(94)00096-J

Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element

Nobito Yamamoto, Mitsuhiro T. Nakao

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

35 Citations (Scopus)

Abstract

The verifications of solutions to weakly nonlinear elliptic equations by the method described e.g. by Nakao (1988, 1989), etc. are sometimes hardly accomplished when the right-hand sides of the equations are very large. To overcome such difficulties, a residual iteration technique with approximate solution was introduced by Nakao (1993). In the present paper, we propose an a posteriori method for the residual iteration, and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element.

Original language	English
Pages (from-to)	271-279
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	60
Issue number	1-2
DOIs	https://doi.org/10.1016/0377-0427(94)00096-J
Publication status	Published - 1995 Jun 20
Externally published	Yes

Keywords

Nonlinear elliptic problem
Numerical verification
Residual iteration

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics

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10.1016/0377-0427(94)00096-J

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AU - Nakao, Mitsuhiro T.

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N2 - The verifications of solutions to weakly nonlinear elliptic equations by the method described e.g. by Nakao (1988, 1989), etc. are sometimes hardly accomplished when the right-hand sides of the equations are very large. To overcome such difficulties, a residual iteration technique with approximate solution was introduced by Nakao (1993). In the present paper, we propose an a posteriori method for the residual iteration, and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element.

AB - The verifications of solutions to weakly nonlinear elliptic equations by the method described e.g. by Nakao (1988, 1989), etc. are sometimes hardly accomplished when the right-hand sides of the equations are very large. To overcome such difficulties, a residual iteration technique with approximate solution was introduced by Nakao (1993). In the present paper, we propose an a posteriori method for the residual iteration, and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element.

KW - Nonlinear elliptic problem

KW - Numerical verification

KW - Residual iteration

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