Mesh adaptivity in finite elements using the mortar method

Authors

  • Christine Bernard Analyse Numerique, B.C. 187, C.N.R.S. & Universite Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris cedex 05
  • Yvon Maday A.S.C.I.-C.N.R.S., Batiment 506, Universite Paris Sud, F-91405 Orsay cedex

Keywords:

Mesh adaptivity, finite elements, mortar method

Abstract

Relying on the mortar element technique, we propose an algorithm for mesh adaptivity in finite elements, where no conformity condition is enforced on the intersection of the triangles during the refinement process. We perform the numerical analysis of the final discretization.

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References

[BE] F. BEN BELGACEM, "Discretisations 30 non conformes par Ia methode de decomposition

de domaine des elements avec joints: analyse mathematique et mise en ceuvre pour le

probleme de Poisson", Thesis. Universite Pierre et Marie Curie, Paris, 1993.

[BG] C. BERNARDI. V. GIRAULT, "A local regularization operator for triangular and quadrilateral

finite elements", SIAM J. Numer. Anal., vol. 35. 1998. 1893-1916.

[BMPI] C. BERNARDI, Y. MADAY, A.T. PATERA, "A new nonconforming approach to domain

decomposition: the mortar element method", College de France Seminar, vol. XI,

H. Brezis & J.-L. Lions eds .. Pitman, 1994, 13-51.

[BMP2) C. BERNARDI. Y. MADAY, A.T. PATERA, "Domain decomposition by the mortar element

method", Asymptotic and Numerical Methods for Partial Differential Equations with

Critical Parameters, H.G. Kaper & M. Garbey eds., N.A.T.O. AS! Series C 384, Kluwer,

269-286.

[BMV] C. BERNARDI, B. METIVET, R. VERFORTH, "Analyse numerique d'indicateurs

d'erreur", Internal Report 93025, Laboratoire d' Analyse Numerique de l'Universite Pierre

et Marie Curie. Paris. 1993.

[GB] P.-L. GEORGE, H. BOROUCHAKI, Triangulation de Delaunay et mail/age. Applications

aux elbnents finis, Editions Hermes, 1997.

[OV] R.G. OWENS, J. VALENCIANO, "An h- p adaptive spectral element method for the

Stokes problem", Proceedings Fourth Int. Conf On Spectral And High Order Methods,

[PS] J. POUSIN, T. SASSI, "A posteriori error estimates and domain decomposition with non

matching grids", submitted to Model. Math. et Anal. Numer.

[VEl] R. YERFORTH, "A posteriori error estimation and adaptive mesh-refinement techniques",

J. Comput. Appl. Math., vol. 50, 1994,67-83.

[VE2) R. VERFORTH. A Review of A Posteriori Error Estimation and Adaptive MeshRefinement

Techniques, Wiley & Teubner. 1996.

[WI] 0.8. WJDLUND, "An extension theorem for finite element spaces with three applications",

Numerical Techniques in Continuum Mechanics, Proceedings of the Second GAMM

Seminar, W. Hackbush & K. Witsch eds., Kiel. 1986.

[WO] B. WOHLMUTH, "A residual based error estimator for mortar finite element discretizations",

Numer. Math., vol. 84, 1999, 143-171.

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Published

2000-04-23

How to Cite

Bernard, C. ., & Maday, Y. . (2000). Mesh adaptivity in finite elements using the mortar method. European Journal of Computational Mechanics, 9(4), 451–465. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/2917

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Original Article