Moving boundary problems (Stefan problems)

• D. den Ouden and L. Zhao and C. Vuik and J. Sietsma and F.J. Vermolen (pdf, bibtex)
  Modelling precipitate nucleation and growth with multiple precipitate species under isothermal conditions: Formulation and analysis
  Computational Materials Science, 79, 933-943, 2013


• C. Vuik (bibtex)
  Phase Change Analysis and Jozef Stefan
  J.C. Crepeau, Editor, Jozef Stefan: His Scientific Legacy on the 175-th Anniversary of His Birth Bentham Science Publishers, Bussum, The Netherlands, 2013


• D. den Ouden and F.J. Vermolen and L. Zhao and C. Vuik and J. Sietsma (bibtex)
  Application of the Level-Set Method to a Mixed-Mode and Curvature Driven Stefan Problem
  Numerical Mathematics and Advanced Applications 2011 Proceedings of ENUMATH 2011 the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011
  Editors: A. Cangiani and R.L. Davidchack and E. Georgoulis and A.N. Gorban and J. Levesley and M.V. Tretyakov
  Springer, Berlin, pp. 141-148, 2013


• D. den Ouden and F.J. Vermolen and L. Zhao and C. Vuik and J. Sietsma (pdf, bibtex)
  Mathematical Modelling of NbC Particle Nucleation and Growth in an HSLA Steel under Elastic Deformation
  Solid State Phenomena, 172-174, pp. 893-898, 2011


• D. den Ouden and F.J. Vermolen and L. Zhao and C. Vuik and J. Sietsma (pdf, bibtex)
  Modelling of particle nucleation and growth in binary alloys under elastic deformation: An application to a Cu-0.95 wt%Co alloy
  Computational Materials Science, 50, pp. 2397-2410, 2011


• E. Javierre and F.J. Vermolen and C. Vuik and S. van der Zwaag (pdf, bibtex)
  A mathematical analysis of physiological and morphological aspects of wound closure
  Journal of Mathematical Biology, 59, pp. 605-630, 2009
  
  
• J.H. Brusche and A. Segal and C. Vuik (pdf, bibtex)
  An efficient numerical method for solid-liquid transitions in optical rewritable recording
  International Journal for Numerical Methods in Engineering, 77, pp. 702-718, 2009
  
  
• F.J. Vermolen and E. Javierre and C. Vuik and L. Zhao and S. van der Zwaag ( pdf , bibtex)
  A three-dimensional model for particle dissolution in binary alloys
  Computational Materials Science, 39, pp. 767-774, 2007
  
  
• E. Javierre and C. Vuik and F.J. Vermolen and A. Segal ( pdf, bibtex)
  A level set method for three dimensional vector Stefan problems: Dissolution of stoichiometric particles in multi-component alloys
  Journal of Computational Physics, 224, pp. 222-240, 2007
  
  
• J.H. Brusche, A. Segal, H.P. Urbach and C. Vuik ( bibtex)
  A Comparison of enthalpy and temperature methods for melting problems on composite domains,
  Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications
  Editors: A. Bermudez de Castro, D. Gomez, P. Quintela, and P. Salgado,
  Springer, Berlin, 2006
  pages 585-592
  
  
• W.O. Dijkstra and C. Vuik and L. Katgerman ( pdf, bibtex )
  Network model of fluid flow in semi-solid Aluminum alloys
  Computational Materials Science, 38 pp. 67-74, 2006
  
  
• E. Javierre and C. Vuik and F.J. Vermolen and S. van der Zwaag ( pdf, bibtex )
  A comparison of models for one-dimensional Stefan problems
  J. Comp. Appl. Math., 192, pp. 445-459, 2006
  
  
• E. Javierre and C. Vuik and F.J. Vermolen and A. Segal ( pdf, bibtex)
  A level set method for particle dissolution in a binary alloy
  Delft University of Technology
  Delft Institute of Applied Mathematics
  Report 05-07
  ISSN 1389-6520
  
  
• W.O. Dijkstra and C. Vuik and L. Katgerman ( pdf, bibtex )
  A direct method of solidification for the enhancement of mushy zone network models
  Materials Science and Engineering: A, 413-414, pp. 255-258, 2005
  
  
• S.P. van der Pijl, A. Segal and C. Vuik ( pdf, bibtex )
  Modelling of three-dimensional bubbly flows with a mass-conserving level-set method
  Computational Fluid and Solid Mechanics, 2005 MIT Conference Proceedings editor: K.J. Bathe, editors Elsevier, Amsterdam, 2005 pages 905-909
  
  
• F.J. Vermolen, C. Vuik, E. Javierre and S. van der Zwaag ( pdf, bibtex )
  Review on some Stefan Problems for Particle Dissolution
  Nonlinear Analysis: Modelling and Control, 10, pp. 257-292, 2005
  
  
• C.W. Kuijpers, F.J. Vermolen, C. Vuik, P.T.G. Koenis, K.E. Nilsen and S. van der Zwaag ( pdf, bibtex )
  The dependence of the beta-AlFeSi to alpha-Al(FeMn)Si transformation kinetics in Al-Mg-Si alloys on the alloying elements
  Materials Science and Engineering A, 394, pp. 9-19, 2005
  
  
• S.P. van der Pijl, A. Segal, C. Vuik, and P. Wesseling ( pdf, bibtex )
  A mass-conserving Level-Set method for modelling of multi-phase flows
  International Journal for Numerical Methods in Fluids, 47, pp. 339--361, 2005
  
  
• F.J. Vermolen and C. Vuik ( pdf-file, bibtex item)
  Solution of vector Stefan problems with cross-diffusion
  Journal of Computational and Applied Mathematics, 176, pp. 179-201,2005
  
  
• F.J. Vermolen and C. Vuik and S. van der Zwaag ( pdf-file, bibtex item)
  Cross-diffusion controlled particle dissolution in metallic alloys
  Computing and Visualization in Science, 8, pp. 27-33,2005
  
  
• S.P. van der Pijl and A. Segal and C. Vuik ( bibtex item)
  Modelling of multi-phase flows with a level-set method
  Numerical Mathematics and Advanced Applications Proceedings of ENUMATH 2003 the 5th European Conference on Numerical Mathematics and Advanced Applications. Prague, August 2003 editor: M. Feistauer and V. Dolejsi and P. Knobloch and K. Najzar, Springer, Berlin, 2004 pages: 698--707 ISBN 3-540-21460-7
  
  
• F. Vermolen and C. Vuik ( pdf-file, bibtex item)
  Numerical solution of vector Stefan problems with cross-diffusion
  Proceedings of the 4th European Congress on Computational Methods in Applied Sciences and Engineering, Volume I, ECCOMAS 2004, Jyvaskyla, Finland, July 24-28, 2004 editor: P. Neittaanmaki and T. Rossi and K. Majava and O. Pironneau University of Jyvaskyla, Jyvaskyla, 2004 pages: CD ISBN 951-39-1868-8
  
  
• S.P. van der Pijl and A. Segal and C. Vuik ( pdf-file, bibtex item)
  A mass conserving level set (MCLS) method for modeling of multi-phase flows
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 03-03
  ISSN 1389-6520
  
  
• N.C.W. Kuijpers, F.J. Vermolen, K. Vuik, and S. van der Zwaag ( pdf-file, bibtex item)
  A model of the beta-AlFeSi to alpha-Al(FeMn)Si transformation in Al-Mg-Si alloys
  Materials Transactions, 44, pp. 1448--1456, 2003
  
  
• F.J. Vermolen and C. Vuik and S. van der Zwaag ( pdf-file, bibtex item)
  Particle dissolution and cross-diffusion in multi-component alloys
  Materials Science and Engineering, A347, pp. 265--279, 2003
  
  
• F.J. Vermolen and C. Vuik and S. van der Zwaag ( pdf-file, bibtex item)
  A mathematical model for the dissolution of stoichiometric particles in multi-component alloys
  Materials Science and Engineering, A328, pp. 14--25, 2002
  
  
• F. Vermolen and C. Vuik and S. van der Zwaag (pdf-file, bibtex item)
  Some mathematical aspects op particle dissolution and cross-diffusion in multi-component alloys
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 01-15
  ISSN 1389-6520
  
  
• W. van Til and C. Vuik and S. van der Zwaag ( bibtex item)
  Moving boundaries in solid state aluminium alloys
  Proceedings Moving Boundaries VI: computational modelling of free and moving boundary problems Lemnos, Greece, May 9-11, 2001, pp. 123--132
  editors: B. Sarler and C.A. Brebbia
  WIT Press, Ashurst, 2001
  
  
• F.J. Vermolen and C. Vuik ( bibtex item)
  A mathematical model for the dissolution of particles in multi-component alloys
  J. Comp. Appl. Math., 126, pp. 233--254, 2000
  see also CWI Report MAS-R9822.
  
  
• W. van Til and C. Vuik and S. van der Zwaag ( bibtex item)
  Comparison of Particle Dissolution Modules in AlStruc (Sintef) and Homog (TUDelft)
  Netherlands Institute for Metals Research
  Technical Report P.00.4.006, 2000
  Delft
  
  
• C. Vuik and G. Segal and F.J. Vermolen ( pdf-file, bibtex item)
  A conserving discretization for a Stefan problem with an interface reaction at the free boundary
  Comput. Visual Sci., 3, pp. 109-114, 2000
  
  
• W. van Til and C. Vuik and S. van der Zwaag ( bibtex item)
  An Inventory of Numerical Methods to model Solid-Solid Phase Transformations
  in Aluminum Alloys (A literature review)
  Netherlands Institute for Metals Research
  Technical Report P.00.4.001, 2000
  Delft
  
  
• F. Vermolen and K. Vuik ( bibtex item)
  A vector valued Stefan problem from aluminium industry
  Nieuw Archief voor Wiskunde, 4e serie, 17, pp. 205-217, 1999
  see also CWI Report MAS-R9814 .
  
  
• F. Vermolen and K. Vuik and S. van der Zwaag ( bibtex item)
  An asymptotic solution for the dissolution of particles in multi-component alloys
  Workshop on phase change with convection modelling and validation, June 24-26, 1999, Warsaw, Poland, pp. 155-159
  editors: T.A. Kowalewski and F. Stella and J. Banaszek and J.S. Szmyd
  Instytut Podstawowych Problemow Techniki, Polskiej Akademii Nauk, Warsaw, 1999
  see also CWI Report MAS-R9822.
  
  
• F. Vermolen and K. Vuik and S. van der Zwaag ( pdf-file, bibtex item)
  A mathematical model for the dissolution kinetics of Mg_2Si-phases in Al-Mg-Si alloys during homogenisation under industrial conditions
  Materials Science and Engineering A, 254, pp. 13-32, 1998
  
  
• F. Vermolen and K. Vuik and S. van der Zwaag ( bibtex item)
  Modelling the microstructural changes during the homogenisation of extrudable Aluminium alloys
  Journal of the Mechanical Behavior of Materials, 9, pp. 115-120, 1998.
  
  
• F. Vermolen and K. Vuik ( pdf-file, bibtex item)
  A numerical method to compute the dissolution of second phases in ternary alloys,
  J. Comp. Appl. Math., 93, pp. 123-143, 1998
  
  
• F. Vermolen and K. Vuik and S. van der Zwaag ( pdf-file, bibtex item)
  The dissolution of a stoichiometric second phase in ternary alloys: A numerical study
  Materials Science and Engineering A, 246, pp. 93-103, 1998
  
  
• Guus Segal, Kees Vuik and Fred Vermolen, ( pdf-file, bibtex item)
  A conserving discretization for the free boundary in a two-dimensional Stefan problem
  J. Comp. Phys., 141, pp. 1-21, 1998.
  See also TUD Report 97-13.
  
  
• F. Vermolen, K. Vuik and S. van der Zwaag
  A numerical analysis for the dissolution of second phase particles in ternary alloys
  Moving Boundaries IV, computational modelling of free and moving boundary problems; pp.153--162
  Proceedings of the fourth international conference on moving boundaries, Gent, August 1997
  editors: R. van Keer and C.A. Brebbia
  Computational Mechanics Publications, Southampton, 1997
  ISBN 1 85312 465 6
  
  
• C. Vuik
  The solution of a one-dimensional Stefan problem
  Centrum voor Wiskunde en Informatica,Amsterdam, 1993,
  CWI-tract 90,
  ISBN 90 6196 419 9
  
  
• C. Vuik ( pdf-file, bibtex)
  Some historical notes about the Stefan problem
  Nieuw Archief voor Wiskunde, 4e serie, 11, pp. 157-167, 1993.
  
  
• C. Vuik
  An L2-error estimate for an approximation of the solution of a parabolic variational inequality
  Numer. Math., 57, pp. 453-471, 1990
  
  
• C. Vuik
  The solutions of a class of Stefan problems
  Thesis, University Utrecht, 1988
  
  
• C. Vuik and C. Cuvelier
  Numerical solution of an etching problem
  J. Comp. Physics, 59, pp. 247-263, 1985.
  
  
• C. Vuik
  Reaktie op:"Is Fick fout?"
  I2 Procestechnologie, 3, pp. 43, 1985.
  
  

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