On variational formulations for the Stokes equations with nonstandard boundary conditions
Bramble, James H. ; Lee, Ping
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994), p. 903-919 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1994__28_7_903_0,
     author = {Bramble, James H. and Lee, Ping},
     title = {On variational formulations for the Stokes equations with nonstandard boundary conditions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {28},
     year = {1994},
     pages = {903-919},
     mrnumber = {1309419},
     zbl = {0819.76063},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1994__28_7_903_0}
}

Bramble, James H.; Lee, Ping. On variational formulations for the Stokes equations with nonstandard boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) pp. 903-919. http://gdmltest.u-ga.fr/item/M2AN_1994__28_7_903_0/

[1] S. Agmon, A. Douglis, L. Nirenberg, 1964, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions II, Comm. Pure Appl. Math., 17, 35-92. | MR 162050 | Zbl 0123.28706

[2] C. Begue, C. Conca, F. Murat, O. Pironneau, 1989, Les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression, Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, Pitman Res. Notes in Math., 181, 179-264. | MR 992649 | Zbl 0687.35069

[3] A. Bendali, J.-M. Dominguez, S. Gallic, 1985, Variational Approach for the Vector Potential Formulation of the Stokes and Navier-Stokes Problems in Three Dimensional Domains, J. Math. Anal, and Appl., 107, 537-560. | MR 787732 | Zbl 0591.35053

[4] J. H. Bramble, J. E. Pasciak, A. H. Schatz, 1986, The construction of Preconditioners for Elliptic Problems by Substructuring, I, Math. Comp. 47, 103-134. | MR 842125 | Zbl 0615.65112

[5] J. H. Bramble, J. E. Pasciak, J. Xu, 1991, Analysis of Multigrid Algorithms with Non-nested Spaces or Non-inherited Quadratic Forms, Math. Comp., 56, 389-414. | Zbl 0699.65075

[6] P. G. Clarlet, 1978, The Finite Element Method in Elliptic Problems, North-Holland, Amsterdam, 1978. | Zbl 0383.65058

[7] J.-M Dominguez, 1983, Formulations en Potential Vecteur du système de Stokes dans un Domaine de R3, Pub. lab. An.Num., L.A., 189, Univ. Paris VI.

[8] K. O. Friedrichs, 1955, Differential forms on Riemannian Manifolds, Comm. Pure Appl. Math., 8, 551-590. | MR 87763 | Zbl 0066.07504

[9] V. Georgescu, 1979, Some Boundary Value Problem for Differential Formson Compact Riemannian Manifolds, Ann. Mat. Para Appl., 122, 159-198. | MR 565068 | Zbl 0432.58026

[10] V. Girault, 1988, Incompressible Finite Element Methods for Navier-Stokes equations with Nonstandard Boundary Conditions in R3, Math. Comp., 51, 55-74. | MR 942143 | Zbl 0666.76053

[11] V. Girault, P.-A. Raviart, 1986, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, Springer-Verlag. | MR 851383 | Zbl 0585.65077

[12] P. Lee, 1990, On the Vector-Scalar Potential Formulation of the Three Dimensional Eddy Current Problem, Thesis, Cornell University.

[13] P. Lee, 1993, A Lagrange Multiplier Method for the Interface Equations from Electromagnetic Applications, SIAM J. Numer. Anal,, 30, 478-507. | MR 1211401 | Zbl 0773.65084

[14] J.-L. Lions, E. Magenes, 1972, Non-homogeneous Boundary Value Problemsand Applications, I, Springer. | Zbl 0223.35039

[15] P. Neittaanmaki, J. Saranen, 1980, Finite Element Approximation of Electromagnetic Fields in Three Dimensional Space, Numer. Funct. Anal. Optimiz., 2, 487-506. | MR 605756 | Zbl 0451.65087

[16] R. Verfurth, 1987, Mixed Finite Element Approximation of the Vector Potential, Numer. Math., 50, 685-695. | MR 884295 | Zbl 0596.76073

[17] R. Temam, 1984, Navier-Stokes Equations, North-Holland. | MR 769654 | Zbl 0568.35002