|
Error indicators for the mortar finite element discretization of the Laplace equation
Author(s):
Christine
Bernardi;
Frédéric
Hecht.
Journal:
Math. Comp.
71
(2002),
1371-1403.
MSC (2000):
Primary 65N30;
Secondary 65N50, 65N55
Posted:
December 4, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
The mortar technique turns out to be well adapted to handle mesh adaptivity in finite elements, since it allows for working with nonnecessarily compatible discretizations on the elements of a nonconforming partition of the initial domain. The aim of this paper is to extend the numerical analysis of residual error indicators to this type of methods for a model problem and to check their efficiency thanks to some numerical experiments.
References:
- 1.
- M. Azaïez, C. Bernardi, Y. Maday -- Some tools for adaptivity in the spectral element method, in Proc. of the third Int. Conf. On Spectral And High Order Methods, Houston J. of Math. (1996), 243-253.
- 2.
- F. Ben Belgacem -- The Mortar finite element method with Lagrange multipliers, Numer. Math. 84 (1999), 173-197. MR 2001b:65101
- 3.
- F. Ben Belgacem, C. Bernardi, N. Chorfi, Y. Maday -- Inf-sup conditions for the mortar spectral element discretization of the Stokes problem, Numer. Math. 85 (2000), 257-281.CMP 2000:12
- 4.
- C. Bernardi, V. Girault -- A local regularization operator for triangular and quadrilateral finite elements, SIAM J. Numer. Anal. 35 (1998), 1893-1916. MR 99g:65107
- 5.
- C. Bernardi, Y. Maday -- Mesh adaptivity in finite elements by the mortar method, Revue européenne des éléments finis 9 (2000), 451-465.
- 6.
- C. Bernardi, Y. Maday, A.T. Patera -- A new nonconforming approach to domain decomposition : the mortar element method, Collège de France Seminar XI, H. Brezis & J.-L. Lions eds., Pitman (1994), 13-51. MR 95a:65201
- 7.
- C. Bernardi, Y. Maday, A.T. Patera -- Domain decomposition by the mortar element method, in Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, H.G. Kaper & M. Garbey eds., N.A.T.O. ASI Series C 384 (1993), 269-286. MR 94c:65151
- 8.
- C. Bernardi, R.G. Owens, J. Valenciano -- An error indicator for mortar element solutions to the Stokes problem, Internal Report 99030, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris (1999).
- 9.
- C. Bernardi, R. Verfürth -- Adaptive finite element methods for elliptic equations with non-smooth coefficients, Numer. Math. 85 (2000), 579-608. MR 2001e:65177
- 10.
- D. Braess, R. Verfürth -- A posteriori error estimators for the Raviart-Thomas element, SIAM J. Numer. Anal. 33 (1996), 2431-2444. MR 97m:65201
- 11.
- F. Bouillault, A. Buffa, Y. Maday, F. Rapetti -- The mortar edge element method in three dimensions: application to magnetostatics, Internal Report, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris (2000).
- 12.
- P.G. Ciarlet -- Basic Error Estimates for Elliptic Problems, in the Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet & J.-L. Lions eds., North-Holland (1991), 17-351. CMP 91:14
- 13.
- P. Clément -- Approximation by finite element functions using local regularization, R.A.I.R.O. Anal. Numér. 9 (1975), 77-84. MR 53:4569
- 14.
- M. Crouzeix -- Personal communication.
- 15.
- F. Hecht, O. Pironneau -- Multiple meshes and the implementation of freefem+, I.N.R.I.A. Report, Rocquencourt (1999).
- 16.
- P. Joly -- Remise en forme, analyse numérique matricielle, Cours de D.E.A., Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris (1999).
- 17.
- J.-L. Lions, E. Magenes -- Problèmes aux limites non homogènes et applications, Vol. 1, Dunod (1968). MR 40:512
- 18.
- L.R. Scott, S. Zhang -- Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comput. 54 (1990), 483-493. MR 90j:65021
- 19.
- R. Verfürth -- A posteriori error estimators for the Stokes equations, II non-conforming discretizations, Numer. Math. 60 (1991), 235-249. MR 92j:65189
- 20.
- R. Verfürth -- A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley & Teubner (1996).
- 21.
- R. Verfürth -- Error estimates for some quasi-interpolation operators, Modél. Math. et Anal. Numér. 33 (1999), 695-713.
- 22.
- O.B. Widlund -- An extension theorem for finite element spaces with three applications, in Numerical Techniques in Continuum Mechanics, Proceedings of the Second GAMM Seminar, W. Hackbush & K. Witsch eds., Kiel (1986).
- 23.
- B. Wohlmuth -- A residual based error estimator for mortar finite element discretizations, Numer. Math. 84 (1999), 143-171. MR 2000h:65155
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(2000):
65N30,
65N50, 65N55
Retrieve articles in all Journals with MSC
(2000):
65N30,
65N50, 65N55
Additional Information:
Christine
Bernardi
Affiliation:
Analyse Numérique, C.N.R.S. et Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
Email:
bernardi@ann.jussieu.fr
Frédéric
Hecht
Affiliation:
Analyse Numérique, C.N.R.S. et Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
Email:
hecht@ann.jussieu.fr
DOI:
10.1090/S0025-5718-01-01401-6
PII:
S 0025-5718(01)01401-6
Received by editor(s):
April 4, 2000
Received by editor(s) in revised form:
October 10, 2000
Posted:
December 4, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org