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 |
Keywords
- Nonlinear elliptic problem
- Numerical verification
- Residual iteration
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
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Yamamoto, N., & Nakao, M. T. (1995). Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element. Journal of Computational and Applied Mathematics, 60(1-2), 271-279. https://doi.org/10.1016/0377-0427(94)00096-J