Finite element methods on non-conforming grids by penalizing the matching constraint

Eric Boillat

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 2, page 357-372
  • ISSN: 0764-583X

Abstract

top
The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

How to cite

top

Boillat, Eric. "Finite element methods on non-conforming grids by penalizing the matching constraint." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 357-372. <http://eudml.org/doc/194168>.

@article{Boillat2010,
abstract = { The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence. },
author = {Boillat, Eric},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite element methods; non-matching grids; penalty technique.; elliptic problems; error estimate; finite element methods; penalty technique},
language = {eng},
month = {3},
number = {2},
pages = {357-372},
publisher = {EDP Sciences},
title = {Finite element methods on non-conforming grids by penalizing the matching constraint},
url = {http://eudml.org/doc/194168},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Boillat, Eric
TI - Finite element methods on non-conforming grids by penalizing the matching constraint
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 357
EP - 372
AB - The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
LA - eng
KW - Finite element methods; non-matching grids; penalty technique.; elliptic problems; error estimate; finite element methods; penalty technique
UR - http://eudml.org/doc/194168
ER -

References

top
  1. R.A. Adams, Sobolev Spaces. Academic Press, New-York, San Francisco, London (1975).  
  2. F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math.84 (1999) 173-197.  Zbl0944.65114
  3. F. Ben Belgacem and Y. Maday, The mortar element method for three dimensional finite elements. RAIRO Modél. Math. Anal. Numér.31 (1997) 289-302.  Zbl0868.65082
  4. M. Bercovier, Perturbation of mixed variational problems. Application to mixed finite element methods. RAIRO Anal. Numér.12 (1978) 211-236.  Zbl0428.65059
  5. F. Brezzi and M. Fortin, Mixed and Hybride Finite Element Methods. Springer-Verlag, New York (1991).  Zbl0788.73002
  6. P.G. Ciarlet, The Finite Element Method for Elliptic Problem. North Holland, Amsterdam (1978).  Zbl0383.65058
  7. P. Clement, Approximation by finite element using local regularization. RAIRO Ser. Rouge8 (1975) 77-84.  Zbl0368.65008
  8. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985).  Zbl0695.35060
  9. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris (1968).  Zbl0165.10801
  10. Y. Maday, C. Bernardi and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Nonlinear Partial Differential Equations and their applications, H. Brezis and J.L. Lions Eds., Vol. XI, Pitman (1994) 13-51.  Zbl0797.65094
  11. J. Nitsche, Über eine Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1970/1971) 9-15.  Zbl0229.65079
  12. D. Schotzau, C. Schwab and R. Stenberg, Mixed hp-fem on anisotropic meshes ii. Hanging nodes and tensor products of boundary layer meshes. Numer. Math.83 (1999) 667-697.  Zbl0958.76049
  13. R. Stenberg, On some techniques for approximating boundary conditions in the finite element method. J. Comput. Appl. Math.63 (1995) 139-148.  Zbl0856.65130

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.