Murea Cornel M, Hentschel H G E
Laboratoire de Mathématiques, Informatique et Applications, Université de Haute-Alsace, 4, rue des Fréres Lumiére, 68093 Mulhouse Cedex, France.
Math Biosci Eng. 2007 Apr;4(2):339-53. doi: 10.3934/mbe.2007.4.339.
We describe finite element simulations of limb growth based on Stokes flow models with a nonzero divergence representing growth due to nutrients in the early stages of limb bud development. We introduce a "tissue pressure" whose spatial derivatives yield the growth velocity in the limb and our explicit time advancing algorithm for such tissue flows is described in de tail. The limb boundary is approached by spline functions to compute the curvature and the unit outward normal vector. At each time step, a mixed hybrid finite element problem is solved, where the condition that the velocity is strictly normal to the limb boundary is treated by a Lagrange multiplier technique. Numerical results are presented.
我们描述了基于斯托克斯流模型的肢体生长有限元模拟，该模型具有非零散度，代表肢体芽发育早期由于营养物质导致的生长。我们引入了一种“组织压力”，其空间导数产生肢体中的生长速度，并详细描述了针对此类组织流动的显式时间推进算法。通过样条函数逼近肢体边界以计算曲率和单位外法向量。在每个时间步，求解一个混合混合有限元问题，其中速度严格垂直于肢体边界的条件通过拉格朗日乘子技术处理。给出了数值结果。
