### Abstract

The immersed boundary (IB) method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. It is characterized by the use of a uniform Cartesian mesh for the fluid, a Lagrangian curvilinear mesh on the elastic material, and discrete delta functions for communication between the two grids. We consider a simple IB problem in a two-dimensional periodic fluid domain with a one-dimensional force generator. We obtain error estimates for the velocity field of the IB solution for the stationary Stokes problem. We use this result to prove convergence of a simple small-amplitude dynamic problem. We test our error estimates against computational experiments.

Original language | English (US) |
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Pages (from-to) | 1213-1263 |

Number of pages | 51 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 61 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2008 |