A finite element method for domain decomposition with non-matching grids

Roland Becker; Peter Hansbo; Rolf Stenberg

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 2, page 209-225
  • ISSN: 0764-583X

Abstract

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In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.

How to cite

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Becker, Roland, Hansbo, Peter, and Stenberg, Rolf. "A finite element method for domain decomposition with non-matching grids." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 209-225. <http://eudml.org/doc/194159>.

@article{Becker2010,
abstract = { In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included. },
author = {Becker, Roland, Hansbo, Peter, Stenberg, Rolf},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nitsche's method; domain decomposition; non-matching grids.; non-matching grids; Poisson problem; error estimates; numerical results; finite element method},
language = {eng},
month = {3},
number = {2},
pages = {209-225},
publisher = {EDP Sciences},
title = {A finite element method for domain decomposition with non-matching grids},
url = {http://eudml.org/doc/194159},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Becker, Roland
AU - Hansbo, Peter
AU - Stenberg, Rolf
TI - A finite element method for domain decomposition with non-matching grids
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 209
EP - 225
AB - In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
LA - eng
KW - Nitsche's method; domain decomposition; non-matching grids.; non-matching grids; Poisson problem; error estimates; numerical results; finite element method
UR - http://eudml.org/doc/194159
ER -

References

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Citations in EuDML Documents

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  1. Christian Grossmann, Penalties, Lagrange multipliers and Nitsche mortaring
  2. Tie Zhu Zhang, Shu Hua Zhang, Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations
  3. Saber Amdouni, Patrick Hild, Vanessa Lleras, Maher Moakher, Yves Renard, A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
  4. Saber Amdouni, Patrick Hild, Vanessa Lleras, Maher Moakher, Yves Renard, A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
  5. Anita Hansbo, Peter Hansbo, Mats G. Larson, A finite element method on composite grids based on Nitsche’s method
  6. Saber Amdouni, Patrick Hild, Vanessa Lleras, Maher Moakher, Yves Renard, A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
  7. Anita Hansbo, Peter Hansbo, Mats G. Larson, A finite element method on composite grids based on Nitsche's method
  8. Carlo D’Angelo, Anna Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids
  9. Carlo D’Angelo, Anna Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids
  10. V. Lleras, A Stabilized Lagrange Multiplier Method for the Finite Element Approximation of Frictional Contact Problems in Elastostatics

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