Accession Number:

ADA556876

Title:

On Convergence of the Immersed Boundary Method for Elliptic Interface Problems

Descriptive Note:

Corporate Author:

NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION

Personal Author(s):

Report Date:

2011-09-29

Pagination or Media Count:

13.0

Abstract:

Peskins Immersed Boundary IB method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics material sciences, and many other areas. Peskins IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the Linfinity norm. But almost none rigorous proof could be found in the literature until recently 9 in which the author showed that the velocity is indeed first order accurate for the Stokes equations with a periodic boundary condition. In this paper, we show the first order convergence with a log h factor of the IB method for elliptic interface problems essential without the boundary condition restrictions. The results should be applicable to the IB method for many different situations involving elliptic solvers for Stokes and Navier-Stokes equations.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE