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A Cut-Cell Finite-Element Method for a Discontinuous Switch Model for Wound Closure

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • S. V. Zemskov

    (Delft University of Technology, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science)

  • F. J. Vermolen

    (Delft University of Technology, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science)

  • E. Javierre

    (Aragón Institute of Engineering Research (I3A), Universidad de Zaragoza, Aragon Health Sciences Institute, Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Group of Structural Mechanics and Materials Modelling (GEMM))

  • C. Vuik

    (Delft University of Technology, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science)

Abstract

A mathematical model for epidermal wound healing is considered. The model is based on a moving boundary problem for the wound edge in which the edge moves if a generic epidermal growth factor exceeds a given threshold value. We use a Galerkin finite-element method to solve the equations for the growth factor concentration. The moving boundary (wound edge) is tracked using a level-set method with a local adaptive mesh refinement in the interface region. To deal with the reaction-diffusion equation for the growth factor, a cut-cell method has been implemented. This cut-cell method warrants the integration over a continuous reaction term elementwisely. The results improved with respect to the results that were obtained without the use of the cut-cell method.

Suggested Citation

  • S. V. Zemskov & F. J. Vermolen & E. Javierre & C. Vuik, 2010. "A Cut-Cell Finite-Element Method for a Discontinuous Switch Model for Wound Closure," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 929-936, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_100
    DOI: 10.1007/978-3-642-11795-4_100
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