Optimal convergence rates of h p mortar finite element methods for second-order elliptic problems

Faker Ben Belgacem; Padmanabhan Seshaiyer; Manil Suri

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 3, page 591-608
  • ISSN: 0764-583X

How to cite

top

Ben Belgacem, Faker, Seshaiyer, Padmanabhan, and Suri, Manil. "Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.3 (2000): 591-608. <http://eudml.org/doc/194004>.

@article{BenBelgacem2000,
author = {Ben Belgacem, Faker, Seshaiyer, Padmanabhan, Suri, Manil},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {optimal convergence; mortar finite element methods; second-order elliptic problems; error estimate; non-conforming finite element method; mortar method},
language = {eng},
number = {3},
pages = {591-608},
publisher = {Dunod},
title = {Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems},
url = {http://eudml.org/doc/194004},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Ben Belgacem, Faker
AU - Seshaiyer, Padmanabhan
AU - Suri, Manil
TI - Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 3
SP - 591
EP - 608
LA - eng
KW - optimal convergence; mortar finite element methods; second-order elliptic problems; error estimate; non-conforming finite element method; mortar method
UR - http://eudml.org/doc/194004
ER -

References

top
  1. [1] Y. Achdou, Y. Maday and O. B. Widlund, Méthode itérative de sous-structuration pour les éléments avec joints. C. R. Acad. Sci. Paris Série I 322 (1996) 185-190. Zbl0836.65118MR1373759
  2. [2] Y. Achdou, Y. Maday and O. B. Widlund, Iterative substructuring preconditioners for the mortar finite element method in two dimensions. SIAM. J. Num. Anal. 36 (1999) 551-580. Zbl0931.65110MR1675257
  3. [3] Y. Achdou and O. Pironneau, A fast solver for Navier-Stokes equations in the laminar regime using mortar finite element and boundary element methods. SIAM. J. Num. Anal. 32 (1995) 985-1016. Zbl0833.76032MR1342280
  4. [4] I. Babuška and M. Suri, The h-p-version of the finite element method with quasi-uniform meshes. Modél. Math. et Anal. Numér. 21 (1987) 199-238. Zbl0623.65113MR896241
  5. [5] I. Babuška and M. Suri, The p and h-p-versions of the finite element method: basic principles and properties. SIAM Review 36 (1984) 578-632. Zbl0813.65118MR1306924
  6. [6] I. Babuška and M. Suri, The optimal convergence rate of the p-Version of the finite element method. SIAM. J. Num. Anal. 24 (1987) 750-776. Zbl0637.65103MR899702
  7. [7] F. Ben Belgacem, Disrétisations 3D non conformes par la méthode de décomposition de domaine des éléments avec joints : Analyse mathématique et mise en oeuvre pour le problème de Poisson. Thèse de l'Université Pierre et Marie Curie, Paris VI. Note technique EDF, ref. HI72/93017 (1993). 
  8. [8] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Num. Mathematik (to appear). Zbl0944.65114MR1730018
  9. [9] F. Ben Belgacem and Y. Maday, Non conforming spectral element methodology tuned to parallel implementation. Compu. Meth. Appl. Mech. Eng. 116 (1994) 59-67. Zbl0841.65096MR1286513
  10. [10] C. Bernardi, N. Débit and Y. Maday, Coupling finite element and spectral methods: first results. Math. Compu. 54 (1990),21-39. Zbl0685.65098MR995205
  11. [11] C. Bernardi, M. Dauge and Y. Maday, Interpolation of nullspaces for polynomial approximation of divergence-free functions in a cube. Proc. Conf. Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge and S. Nicaise Eds., Lecture Notes in Pure and Applied Mathematics 167 Dekker (1994) 27-46. Zbl0830.46015MR1301339
  12. [12] C. Bernardi and Y. Maday, Spectral, spectral element and mortar element methods. Technical report of the Laboratoire d'analyse numérique, Université Pierre et Marie Curie, Paris VI, 1998. Zbl0991.65124
  13. [13] C. Bernardi and Y. Maday, Relèvement de traces polynomiales et applications. RAIRO Modél. Math. Anal. Numér. 24 (1990)557-611. Zbl0707.65077MR1076961
  14. [14] C. Bernardi, Y. Maday and A. T. Patera, A new non conforming approach to domain décomposition: The mortar element method. Pitman, H. Brezis, J.-L. Lions Eds., Collège de France Seminar (1990). Zbl0797.65094
  15. [15] C. Bernardi, Y. Maday and G. Sacchi-Landriam, Non conforming matching conditions for coupling spectral and finite element methods. Appl. Numer. Math. 54 (1989) 64-84. Zbl0684.65099MR1045019
  16. [16] A. Berger, R. Scott and G. Strang, Approximate boundary conditions in the finite element method. Symposia Mathematica 10 (1972) 295-313. Zbl0266.73050MR403258
  17. [17] S. Brenner, A non-standard finite element interpolation estimate. Research Report 1998:07, Department of Mathematics, University of South Carohna (1998). Zbl0938.65133
  18. [18] P.-G. Ciarlet, The finite element Method for Elliptic Problems. North Holland (1978). Zbl0383.65058MR520174
  19. [19] N. Débit, La méthode des éléments avec joints dans le cas du couplage des méthodes spectrales et méthodes des éléments finis : Résolution des équations de Navier-Stokes. Thèse de l'Université Pierre et Marie Curie, Paris VI (1992). 
  20. [20] M. Dorr, On the discretization of inter-domain coupling in elliptic boundary-value problems via the p-Version of the finite element method. T. F. Chan, R. Glowinski, J. Périaux. O.B. Widlund, Eds., SIAM (1989). Zbl0682.65068MR992001
  21. [21] V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations. Springer Verlag (1986). Zbl0585.65077MR851383
  22. [22] P. Grisvard, Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics 24 (Pitman, 1985). Zbl0695.35060MR775683
  23. [23] W. Gui and I. Babuška, The h-p-version of the finite element method in one dimension. Num. Mathematik 3 (1986) 577-657. Zbl0614.65088MR861522
  24. [24] B. Guo and I. Babuška, The h-p-version of the finite element method. Compu. Mech. 1 (1986), Part 1: 21-41, Part 2:203-220. Zbl0634.73059
  25. [25] P. Seshaiyer, Non-Conjorming h-p finite element methods. Doctoral Thesis, University of Maryland Baltimore County (1998). 
  26. [26] P. Seshaiyer and M. Suri, Uniform h-p Convergence results for the mortar finite element method. Math. Compu. PII: S0025-5718(99)01083-2 (to appear). Zbl0944.65113MR1649643
  27. [27] P. Seshaiyer and M. Suri, Convergence results for the non-Conforming h-p methods. The mortar finite element method. AMS, Cont. Math. 218 (1998) 467-473. Zbl0909.65075MR1649643
  28. [28] P. Seshaiyer and M. Suri, h-p submeshing via non-conforming finite element methods. Submitted to Compu. Meth. Appl. Mech. Eng. (1998). Zbl0971.65101
  29. [29] G. Strang and G. J. Fix, An analysis of the finite element method. Wellesly, Cambridge Press Masson (1973). Zbl0356.65096MR443377

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.