On Convergence of the Immersed Boundary Method for Elliptic Interface Problems

Abstract

Peskin's 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. Peskin's IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the L(infinity) 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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 29, 2011
Accession Number
ADA556876

Entities

People

  • Zhilin Li

Organizations

  • North Carolina State University

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Computational Science
  • Convergence
  • Delta Functions
  • Difference Equations
  • Differential Equations
  • Equations
  • Errors
  • Fluid Mechanics
  • Integrals
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Partial Differential Equations
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.