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

Norikazu Saito, Yoshiki Sugitani

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)181-199
ページ数19
ジャーナルNumerical Methods for Partial Differential Equations
35
1
DOI
出版ステータスPublished - 2019 1

ASJC Scopus subject areas

  • 分析
  • 数値解析
  • 計算数学
  • 応用数学

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