Analysis of the immersed boundary method for a finite element Stokes problem

Norikazu Saito, Yoshiki Sugitani

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Convergence results are presented for the immersed boundary (IB) method applied to a model Stokes problem. As a discretization method, we use the finite element method. First, the immersed force field is approximated using a regularized delta function. Its error in the W−1, p norm is examined for 1 ≤ p < n/(n − 1), with n representing the space dimension. Subsequently, we consider IB discretization of the Stokes problem and examine the regularization and discretization errors separately. Consequently, error estimate of order h1 − α in the W1, 1 × L1 norm for the velocity and pressure is derived, where α is an arbitrary small positive number. The validity of those theoretical results is confirmed from numerical examples.

Original languageEnglish
Pages (from-to)181-199
Number of pages19
JournalNumerical Methods for Partial Differential Equations
Volume35
Issue number1
DOIs
Publication statusPublished - 2019 Jan

Keywords

  • Stokes equation
  • finite element method
  • immersed boundary method

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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