On the CFL condition for the finite element immersed boundary method

The finite element version of the immersed boundary method proved to be a robust alternative to the original one which was based on finite differences. In this paper we highlight the advantages of the new method and discuss a stability analysis for its space-time discretization. Numerical experiments confirm the theoretical results.

[1]  R. Rannacher,et al.  Finite element approximation of the nonstationary Navier-Stokes problem. I : Regularity of solutions and second-order error estimates for spatial discretization , 1982 .

[2]  Charles S. Peskin,et al.  Stability and Instability in the Computation of Flows with Moving Immersed Boundaries: A Comparison of Three Methods , 1992, SIAM J. Sci. Comput..

[3]  Charles S. Peskin,et al.  Fluid Flow in Collapsible Elastic Tubes: A Three-Dimensional Numerical Model , 2001 .

[4]  Wing Kam Liu,et al.  Extended immersed boundary method using FEM and RKPM , 2004 .

[5]  L. Heltai,et al.  Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method , 2006 .

[6]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[7]  D. Boffi,et al.  The immersed boundary method: a finite element approach , 2003 .

[8]  C. Peskin.  Acta Numerica 2002: The immersed boundary method , 2002 .

[9]  C. Peskin,et al.  Heart Simulation by an Immersed Boundary Method with Formal Second-order Accuracy and Reduced Numerical Viscosity , 2001 .

[10]  L. Heltai,et al.  Stability results for the finite element approach to the immersed boundary method , 2005 .

[11]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[12]  Lucy T. Zhang,et al.  Immersed finite element method , 2004 .

[13]  Arieh Iserles,et al.  Acta Numerica 2002 , 2002 .

[14]  L. Heltai,et al.  A finite element approach to the immersed boundary method , 2003 .

[15]  L. Heltai.  On the stability of the finite element immersed boundary method , 2008 .

[16]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[17]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[18]  L. Heltai,et al.  Mathematical Models and Methods in Applied Sciences Vol. 17, No. 10 (17) 1479–1505 c ○ World Scientific Publishing Company NUMERICAL STABILITY OF THE FINITE ELEMENT IMMERSED BOUNDARY METHOD , 2005 .

[19]  C. Peskin,et al.  A three-dimensional computational method for blood flow in the heart. 1. Immersed elastic fibers in a viscous incompressible fluid , 1989 .