Abstract
We propose two methods to enclose the solution of an ordinary free boundary problem. The problem is reformulated as a nonlinear boundary value problem on a fixed interval including an unknown parameter. By appropriately setting a functional space that depends on the finite element approximation, the solution is represented as a fixed point of a compact map. Then, by using the finite element projection with constructive error estimates, a Newton-type verification procedure is derived. In addition, numerical examples confirming the effectiveness of current methods are given.
| Original language | English |
|---|---|
| Pages (from-to) | 523-542 |
| Number of pages | 20 |
| Journal | Numerical Functional Analysis and Optimization |
| Volume | 26 |
| Issue number | 4-5 |
| DOIs | |
| Publication status | Published - 2005 |
| Externally published | Yes |
Fingerprint
Keywords
- Enclosure methods
- Free boundary
- Numerical verification methods
ASJC Scopus subject areas
- Applied Mathematics
- Control and Optimization
Cite this
Numerical verification methods for solutions of the free boundary problem. / Hashimoto, Kouji; Kobayashi, Kenta; Nakao, Mitsuhiro T.
In: Numerical Functional Analysis and Optimization, Vol. 26, No. 4-5, 2005, p. 523-542.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Numerical verification methods for solutions of the free boundary problem
AU - Hashimoto, Kouji
AU - Kobayashi, Kenta
AU - Nakao, Mitsuhiro T.
PY - 2005
Y1 - 2005
N2 - We propose two methods to enclose the solution of an ordinary free boundary problem. The problem is reformulated as a nonlinear boundary value problem on a fixed interval including an unknown parameter. By appropriately setting a functional space that depends on the finite element approximation, the solution is represented as a fixed point of a compact map. Then, by using the finite element projection with constructive error estimates, a Newton-type verification procedure is derived. In addition, numerical examples confirming the effectiveness of current methods are given.
AB - We propose two methods to enclose the solution of an ordinary free boundary problem. The problem is reformulated as a nonlinear boundary value problem on a fixed interval including an unknown parameter. By appropriately setting a functional space that depends on the finite element approximation, the solution is represented as a fixed point of a compact map. Then, by using the finite element projection with constructive error estimates, a Newton-type verification procedure is derived. In addition, numerical examples confirming the effectiveness of current methods are given.
KW - Enclosure methods
KW - Free boundary
KW - Numerical verification methods
UR - http://www.scopus.com/inward/record.url?scp=27744555836&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=27744555836&partnerID=8YFLogxK
U2 - 10.1080/01630560500248314
DO - 10.1080/01630560500248314
M3 - Article
AN - SCOPUS:27744555836
VL - 26
SP - 523
EP - 542
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
SN - 0163-0563
IS - 4-5
ER -