On the stability of the finite element immersed boundary method

Authors:
Luca Heltai
Affiliations:
Dipartimento di Matematica "F. Casorati", Via Ferrata 1, I-27100 Pavia, Italy
Venue:
Computers and Structures
Year:
2008

Citing 12
Cited 1

A three-dimensional computational method for blood flow in the heart. 1. Immersed elastic fibers in a viscous incompressible fluid

Journal of Computational Physics
Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods

SIAM Journal on Scientific and Statistical Computing
Improved volume conservation in the computation of flows with immersed elastic boundaries

Journal of Computational Physics
Stability analysis for the immersed fiber problem

SIAM Journal on Applied Mathematics
Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes

Journal of Computational Physics
The blob projection method for immersed boundary problems

Journal of Computational Physics
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method

Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations

SIAM Journal on Scientific Computing
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems

Journal of Computational Physics
On the CFL condition for the finite element immersed boundary method

Computers and Structures

On the stability of the Immersed Finite Element Method with high order structural elements

Computers and Structures

Quantified Score

Hi-index	0.00

Visualization

Abstract

The immersed boundary (IB) method is a mathematical formulation for fluid-structure interaction problems, where immersed incompressible visco-elastic bodies or boundaries interact with an incompressible fluid. The original numerical scheme associated to the IB method requires a smoothed approximation of the Dirac delta distribution to link the moving Lagrangian domain with the fixed Eulerian one. We present a stability analysis of the finite element immersed boundary method, where the Dirac delta distribution is treated variationally, in a generalized visco-elastic framework and for two different time-stepping schemes.