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 | |
| Publication status | Published - 1995 Jun 20 |
| Externally published | Yes |
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Keywords
- Nonlinear elliptic problem
- Numerical verification
- Residual iteration
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
Cite this
Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element. / Yamamoto, Nobito; Nakao, Mitsuhiro T.
In: Journal of Computational and Applied Mathematics, Vol. 60, No. 1-2, 20.06.1995, p. 271-279.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element
AU - Yamamoto, Nobito
AU - Nakao, Mitsuhiro T.
PY - 1995/6/20
Y1 - 1995/6/20
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
UR - http://www.scopus.com/inward/record.url?scp=0000566179&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000566179&partnerID=8YFLogxK
U2 - 10.1016/0377-0427(94)00096-J
DO - 10.1016/0377-0427(94)00096-J
M3 - Article
VL - 60
SP - 271
EP - 279
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 1-2
ER -