Numerical analysis of a Stokes interface problem based on formulation using the characteristic function

Yoshiki Sugitani

Applications of Mathematics (2017)

  • Volume: 62, Issue: 5, page 459-476
  • ISSN: 0862-7940

Abstract

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Numerical analysis of a model Stokes interface problem with the homogeneous Dirichlet boundary condition is considered. The interface condition is interpreted as an additional singular force field to the Stokes equations using the characteristic function. The finite element method is applied after introducing a regularization of the singular source term. Consequently, the error is divided into the regularization and discretization parts which are studied separately. As a result, error estimates of order h 1 / 2 in H 1 × L 2 norm for the velocity and pressure, and of order h in L 2 norm for the velocity are derived. Those theoretical results are also verified by numerical examples.

How to cite

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Sugitani, Yoshiki. "Numerical analysis of a Stokes interface problem based on formulation using the characteristic function." Applications of Mathematics 62.5 (2017): 459-476. <http://eudml.org/doc/294128>.

@article{Sugitani2017,
abstract = {Numerical analysis of a model Stokes interface problem with the homogeneous Dirichlet boundary condition is considered. The interface condition is interpreted as an additional singular force field to the Stokes equations using the characteristic function. The finite element method is applied after introducing a regularization of the singular source term. Consequently, the error is divided into the regularization and discretization parts which are studied separately. As a result, error estimates of order $h^\{1/2\}$ in $H^1\times L^2$ norm for the velocity and pressure, and of order $h$ in $L^2$ norm for the velocity are derived. Those theoretical results are also verified by numerical examples.},
author = {Sugitani, Yoshiki},
journal = {Applications of Mathematics},
keywords = {interface problem; Stokes equation; finite element method},
language = {eng},
number = {5},
pages = {459-476},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical analysis of a Stokes interface problem based on formulation using the characteristic function},
url = {http://eudml.org/doc/294128},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Sugitani, Yoshiki
TI - Numerical analysis of a Stokes interface problem based on formulation using the characteristic function
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 5
SP - 459
EP - 476
AB - Numerical analysis of a model Stokes interface problem with the homogeneous Dirichlet boundary condition is considered. The interface condition is interpreted as an additional singular force field to the Stokes equations using the characteristic function. The finite element method is applied after introducing a regularization of the singular source term. Consequently, the error is divided into the regularization and discretization parts which are studied separately. As a result, error estimates of order $h^{1/2}$ in $H^1\times L^2$ norm for the velocity and pressure, and of order $h$ in $L^2$ norm for the velocity are derived. Those theoretical results are also verified by numerical examples.
LA - eng
KW - interface problem; Stokes equation; finite element method
UR - http://eudml.org/doc/294128
ER -

References

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