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Volume 16, Issue 6
Distributed Lagrange Multiplier-Fictitious Domain Finite Element Method for Stokes Interface Problems

Andrew Lundberg, Pengtao Sun & Cheng Wang

Int. J. Numer. Anal. Mod., 16 (2019), pp. 939-963.

Published online: 2019-08

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  • Abstract

In this paper, the distributed Lagrange multiplier-fictitious domain (DLM/FD) finite element method is studied for a type of steady state Stokes interface problems with jump coefficients, and its well-posedness, stability and optimal convergence properties are analyzed by proving an $inf$-$sup$ condition for a nested saddle-point problem that is induced by both Stokes equations and DLM/FD method in regard to Stokes variables (velocity and pressure) and Lagrange multipliers. Numerical experiments validate the obtained convergence theorem of DLM/FD finite element method for Stokes interface problems with respect to different jump ratios.

  • Keywords

Stokes interface problems, jump coefficients, distributed Lagrange multiplier, fictitious domain method, mixed finite element, well-posedness, error estimates.

  • AMS Subject Headings

65N30, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lundber7@unlv.nevada.edu (Andrew Lundberg)

pengtao.sun@unlv.edu (Pengtao Sun)

wangcheng@tongji.edu.cn (Cheng Wang)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-939, author = {Lundberg , AndrewSun , Pengtao and Wang , Cheng}, title = {Distributed Lagrange Multiplier-Fictitious Domain Finite Element Method for Stokes Interface Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {6}, pages = {939--963}, abstract = {

In this paper, the distributed Lagrange multiplier-fictitious domain (DLM/FD) finite element method is studied for a type of steady state Stokes interface problems with jump coefficients, and its well-posedness, stability and optimal convergence properties are analyzed by proving an $inf$-$sup$ condition for a nested saddle-point problem that is induced by both Stokes equations and DLM/FD method in regard to Stokes variables (velocity and pressure) and Lagrange multipliers. Numerical experiments validate the obtained convergence theorem of DLM/FD finite element method for Stokes interface problems with respect to different jump ratios.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13261.html} }
TY - JOUR T1 - Distributed Lagrange Multiplier-Fictitious Domain Finite Element Method for Stokes Interface Problems AU - Lundberg , Andrew AU - Sun , Pengtao AU - Wang , Cheng JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 939 EP - 963 PY - 2019 DA - 2019/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13261.html KW - Stokes interface problems, jump coefficients, distributed Lagrange multiplier, fictitious domain method, mixed finite element, well-posedness, error estimates. AB -

In this paper, the distributed Lagrange multiplier-fictitious domain (DLM/FD) finite element method is studied for a type of steady state Stokes interface problems with jump coefficients, and its well-posedness, stability and optimal convergence properties are analyzed by proving an $inf$-$sup$ condition for a nested saddle-point problem that is induced by both Stokes equations and DLM/FD method in regard to Stokes variables (velocity and pressure) and Lagrange multipliers. Numerical experiments validate the obtained convergence theorem of DLM/FD finite element method for Stokes interface problems with respect to different jump ratios.

Lundberg , AndrewSun , Pengtao and Wang , Cheng. (2019). Distributed Lagrange Multiplier-Fictitious Domain Finite Element Method for Stokes Interface Problems. International Journal of Numerical Analysis and Modeling. 16 (6). 939-963. doi:
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