A finite element method on composite grids based on Nitsche’s method

Anita Hansbo; Peter Hansbo; Mats G. Larson

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 3, page 495-514
  • ISSN: 0764-583X

Abstract

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In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.

How to cite

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Hansbo, Anita, Hansbo, Peter, and Larson, Mats G.. "A finite element method on composite grids based on Nitsche’s method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.3 (2003): 495-514. <http://eudml.org/doc/245706>.

@article{Hansbo2003,
abstract = {In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.},
author = {Hansbo, Anita, Hansbo, Peter, Larson, Mats G.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Nitsche’s method; overlapping grids; finite element method; penality method; Poisson equation},
language = {eng},
number = {3},
pages = {495-514},
publisher = {EDP-Sciences},
title = {A finite element method on composite grids based on Nitsche’s method},
url = {http://eudml.org/doc/245706},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Hansbo, Anita
AU - Hansbo, Peter
AU - Larson, Mats G.
TI - A finite element method on composite grids based on Nitsche’s method
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 3
SP - 495
EP - 514
AB - In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
LA - eng
KW - Nitsche’s method; overlapping grids; finite element method; penality method; Poisson equation
UR - http://eudml.org/doc/245706
ER -

References

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  9. [9] A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg. 191 (2002) 5537–5552. Zbl1035.65125
  10. [10] R.D. Lazarov, J.E. Pasciak, J. Schöberl and P.S. Vassilevski, Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids. Technical Report, ISC-01-05-MATH (2001). Zbl1095.65103
  11. [11] R.D. Lazarov, S.Z. Tomov and P.S. Vassilevski, Interior penalty discontinuous approximations of elliptic problems. Comput. Meth. Appl. Math. 1 (2001) 367–382. Zbl0995.65114
  12. [12] J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9–15. Zbl0229.65079
  13. [13] L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 190 (1990) 483–493. Zbl0696.65007
  14. [14] R. Stenberg, Mortaring by a method of J.A. Nitsche, in Computational Mechanics: New Trends and Applications, S. Idelsohn, E. Onate and E. Dvorkin Eds., CIMNE, Barcelona (1998). MR1839048

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