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
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U2 - 10.1080/01630560500248314
DO - 10.1080/01630560500248314
M3 - Article
AN - SCOPUS:27744555836
SN - 0163-0563
VL - 26
SP - 523
EP - 542
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
IS - 4-5
ER -