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 |
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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