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- Title
Analysis of the immersed boundary method for a finite element Stokes problem.
- Authors
Saito, Norikazu; Sugitani, Yoshiki
- 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.
- Subjects
FINITE element method; MATHEMATICAL regularization; DISCRETIZATION methods; BOUNDARY value problems; STOKES equations
- Publication
Numerical Methods for Partial Differential Equations, 2019, Vol 35, Issue 1, p181
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22296