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Numerical Algorithms for Free Boundary Problems of Obstacle Types
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH , 2009. , vii, 24 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 09:02
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-10930ISBN: 978-91-7415-353-8 (print)OAI: oai:DiVA.org:kth-10930DiVA: diva2:232665
Public defence
2009-08-20, Sal H1, Teknikringen 31, KTH, Stockholm, 14:00 (English)
Opponent
Supervisors
Note
QC 20100706Available from: 2009-08-25 Created: 2009-08-25 Last updated: 2010-07-06Bibliographically approved
List of papers
1. Numerical algorithm for spatial segregation of competitive systems
Open this publication in new window or tab >>Numerical algorithm for spatial segregation of competitive systems
2009 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, no 5, 3946-3958 p.Article in journal (Refereed) Published
Abstract [en]

Two novel iterative methods for a class of population models of competitive type are considered. This numerical solution is related to the positive solution as the competitive rate tends to infinity. Furthermore, the idea first is applied to an optimal partition problem.

Keyword
free boundary problems, competing species, finite element, DIFFUSION SYSTEMS, ELLIPTIC-SYSTEMS, NODAL DOMAINS
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13971 (URN)10.1137/080722588 (DOI)000271747300032 ()2-s2.0-79960118114 (Scopus ID)
Note
QC 20100705Available from: 2010-07-06 Created: 2010-07-06 Last updated: 2017-12-12Bibliographically approved
2. Perturbation formula of the two-phase membrane problem
Open this publication in new window or tab >>Perturbation formula of the two-phase membrane problem
(English)Article in journal (Other academic) Submitted
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13972 (URN)
Note
QC 20100706Available from: 2010-07-06 Created: 2010-07-06 Last updated: 2010-07-21Bibliographically approved
3. Numerical solutions of the two-phase membrane problem
Open this publication in new window or tab >>Numerical solutions of the two-phase membrane problem
2011 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 61, no 1, 92-107 p.Article in journal (Refereed) Published
Abstract [en]

In this paper different numerical methods for a two-phase free boundary problem are discussed. In the first method a novel iterative scheme for the two-phase membrane is considered. We study the regularization method and give an a posteriori error estimate which is needed for the implementation of the regularization method. Moreover, an efficient algorithm based on the finite element method is presented. It is shown that the sequence constructed by the algorithm is monotone and converges to the solution of the given free boundary problem. These methods can be applied for the one-phase obstacle problem as well.

Keyword
Free boundary problems, Two-phase membrane, Finite element method, Error estimate, Regularization
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13974 (URN)10.1016/j.apnum.2010.08.007 (DOI)000284792500007 ()
Note
Updated from submitted to published. QC 20120327Available from: 2010-07-06 Created: 2010-07-06 Last updated: 2017-12-12Bibliographically approved
4. Numerical solution of the m-membranes problem
Open this publication in new window or tab >>Numerical solution of the m-membranes problem
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13975 (URN)
Note
QC 20100706Available from: 2010-07-06 Created: 2010-07-06 Last updated: 2010-07-21Bibliographically approved

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  • Other locale
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