Optimal convergence rates of hp mortar finite element methods for second-order elliptic problems
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 3, pp. 591-608.
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     title = {Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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     url = {http://archive.numdam.org/item/M2AN_2000__34_3_591_0/}
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Ben Belgacem, Faker; Seshaiyer, Padmanabhan; Suri, Manil. Optimal convergence rates of $hp$ mortar finite element methods for second-order elliptic problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 3, pp. 591-608. http://archive.numdam.org/item/M2AN_2000__34_3_591_0/

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Num. Mathematik (to appear). | MR | Zbl

[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. | MR | Zbl

[10] C. Bernardi, N. Débit and Y. Maday, Coupling finite element and spectral methods: first results. Math. Compu. 54 (1990),21-39. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[13] C. Bernardi and Y. Maday, Relèvement de traces polynomiales et applications. RAIRO Modél. Math. Anal. Numér. 24 (1990)557-611. | Numdam | MR | Zbl

[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). | Zbl

[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. | MR | Zbl

[16] A. Berger, R. Scott and G. Strang, Approximate boundary conditions in the finite element method. Symposia Mathematica 10 (1972) 295-313. | MR | Zbl

[17] S. Brenner, A non-standard finite element interpolation estimate. Research Report 1998:07, Department of Mathematics, University of South Carohna (1998). | Zbl

[18] P.-G. Ciarlet, The finite element Method for Elliptic Problems. North Holland (1978). | MR | Zbl

[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] 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). | MR | Zbl

[21] V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations. Springer Verlag (1986). | MR | Zbl

[22] P. Grisvard, Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics 24 (Pitman, 1985). | MR | Zbl

[23] W. Gui and I. Babuška, The h-p-version of the finite element method in one dimension. Num. Mathematik 3 (1986) 577-657. | MR | Zbl

[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. | Zbl

[25] P. Seshaiyer, Non-Conjorming h-p finite element methods. Doctoral Thesis, University of Maryland Baltimore County (1998).

[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). | MR | Zbl

[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. | MR

[28] P. Seshaiyer and M. Suri, h-p submeshing via non-conforming finite element methods. Submitted to Compu. Meth. Appl. Mech. Eng. (1998). | Zbl

[29] G. Strang and G. J. Fix, An analysis of the finite element method. Wellesly, Cambridge Press Masson (1973). | MR | Zbl