# A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation

J. Zhu; Y.-T. Zhang; S. A. Newman; M. S. Alber

Mathematical Modelling of Natural Phenomena (2009)

- Volume: 4, Issue: 4, page 131-148
- ISSN: 0973-5348

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topZhu, J., et al. "A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation." Mathematical Modelling of Natural Phenomena 4.4 (2009): 131-148. <http://eudml.org/doc/222349>.

@article{Zhu2009,

abstract = {
Skeletal patterning in the vertebrate limb,
i.e., the spatiotemporal regulation of cartilage differentiation
(chondrogenesis) during embryogenesis and regeneration, is one
of the best studied examples of a multicellular developmental process.
Recently [Alber et al., The morphostatic limit for a model of
skeletal pattern formation in the vertebrate limb, Bulletin of
Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation
reaction-diffusion system was developed to describe the interaction of two of
the key morphogens: the activator and an activator-dependent inhibitor of
precartilage condensation formation. A discontinuous Galerkin (DG)
finite element method was applied to solve this nonlinear system on complex
domains to study the effects of domain geometry on the pattern generated [Zhu et
al., Application of Discontinuous Galerkin Methods for reaction-diffusion
systems in developmental biology, Journal of Scientific Computing, 2009, v40,
pp. 391-418]. In this paper, we extend these previous results and develop a DG
finite element model in a moving and deforming domain for skeletal pattern
formation in the vertebrate limb. Simulations reflect the actual dynamics of
limb development and indicate the important role played by the geometry
of the undifferentiated apical zone.
},

author = {Zhu, J., Zhang, Y.-T., Newman, S. A., Alber, M. S.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {discontinuous Galerkin finite element methods; reaction-diffusion
equations; operator splitting; triangular meshes; moving domain; complex
geometry; limb development; reaction-diffusion equations; complex geometry},

language = {eng},

month = {7},

number = {4},

pages = {131-148},

publisher = {EDP Sciences},

title = {A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation},

url = {http://eudml.org/doc/222349},

volume = {4},

year = {2009},

}

TY - JOUR

AU - Zhu, J.

AU - Zhang, Y.-T.

AU - Newman, S. A.

AU - Alber, M. S.

TI - A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation

JO - Mathematical Modelling of Natural Phenomena

DA - 2009/7//

PB - EDP Sciences

VL - 4

IS - 4

SP - 131

EP - 148

AB -
Skeletal patterning in the vertebrate limb,
i.e., the spatiotemporal regulation of cartilage differentiation
(chondrogenesis) during embryogenesis and regeneration, is one
of the best studied examples of a multicellular developmental process.
Recently [Alber et al., The morphostatic limit for a model of
skeletal pattern formation in the vertebrate limb, Bulletin of
Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation
reaction-diffusion system was developed to describe the interaction of two of
the key morphogens: the activator and an activator-dependent inhibitor of
precartilage condensation formation. A discontinuous Galerkin (DG)
finite element method was applied to solve this nonlinear system on complex
domains to study the effects of domain geometry on the pattern generated [Zhu et
al., Application of Discontinuous Galerkin Methods for reaction-diffusion
systems in developmental biology, Journal of Scientific Computing, 2009, v40,
pp. 391-418]. In this paper, we extend these previous results and develop a DG
finite element model in a moving and deforming domain for skeletal pattern
formation in the vertebrate limb. Simulations reflect the actual dynamics of
limb development and indicate the important role played by the geometry
of the undifferentiated apical zone.

LA - eng

KW - discontinuous Galerkin finite element methods; reaction-diffusion
equations; operator splitting; triangular meshes; moving domain; complex
geometry; limb development; reaction-diffusion equations; complex geometry

UR - http://eudml.org/doc/222349

ER -

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