no. 6
Divergence stability in connection with the p-version of the finite element method
ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 6, pp. 737-764. 
@article{M2AN_1990__24_6_737_0,
     author = {Jensen, S. and Vogelius, M.},
     title = {Divergence stability in connection with the $p$-version of the finite element method},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {737--764},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {24},
     number = {6},
     year = {1990},
     mrnumber = {1080717},
     zbl = {0717.65085},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1990__24_6_737_0/}
}
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Jensen, S.; Vogelius, M. Divergence stability in connection with the $p$-version of the finite element method. ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 6, pp. 737-764. http://archive.numdam.org/item/M2AN_1990__24_6_737_0/

[1] D. N. Arnold , L. R. Scott and M. Vogelius, Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Annali Scuola Norm. Sup. Pisa, Serie 4, 15 (1988), pp. 169-192. | EuDML | Numdam | MR | Zbl

[2] I. Babuška, Error-bounds for the finite element method. Numerische Mathematik, 16 (1971), pp. 322-333. | EuDML | MR | Zbl

[3] I. Babuška, B. A. Szabo and I. N. Katz, The p-version of the finite element method. SIAM J. Numer. Anal., 18 (1981), pp. 515-545. | MR | Zbl

[4] M. Bercovier and O. Pironneau, Error estimates for the finite element method solution of the Stokes problem in the primitive variables. Numerische Mathematik, 33 (1979), pp. 211-224. | EuDML | MR | Zbl

[5] J. Boland and R. A. Nicolaides, On the stability of Bilinear-Constant Velocity-Pressure Finite Elements. Numerische Mathematik, 44 (1984), pp. 219-222. | EuDML | MR | Zbl

[6] J. Boland and R. A. Nicolaides, Stable and semistable low order finite elements for viscous flows. SIAM J. Numer. Anal., 22 (1985), pp. 474-492. | MR | Zbl

[7] F. Brezzi, On the existence, uniqueness and approximation of saddlepoint problems arising from Lagrangian multipliers, RAIRO 8 (1974), pp. 129-151. | EuDML | Numdam | MR | Zbl

[8] C. Canuto , Y. Maday and A. Quarteroni, Combined Finite Element and Spectral approximation of the Navier-Stokes equations. Numerische Mathematik, 44 (1984), pp. 201-217. | EuDML | MR | Zbl

[9] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms. Springer-Verlag, 1986. | MR | Zbl

[10] D. Gottlieb and S. Orszag, Numerical Analysis of Spectral Methods : Theory and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics, 26. SIAM, 1977. | MR | Zbl

[11] P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, 1985. | MR | Zbl

[12] C. Johnson and J. Pitkäranta, Analysis of some mixed finite element methods related to reduced integration. Math, of Comp., 38 (1982), pp. 375-400. | MR | Zbl

[13] R. B. Kellogg and J. E. Osborn, A regularity result for the Stokes problem in a convex polygon. J. Functional Analysis, 21 (1976), pp. 397-431. | MR | Zbl

[14] N. N. Lebedev, Special Functions and Their Applications, Prentice-Hall, 1965. | MR | Zbl

[15] Y. Maday, Analysis of spectral projectors in multi-dimensional domains.

[16] E. M. Ronquist, Optimal spectral element method for the unsteady three-dimensional incompressible Navier-Stokes equations. Ph. D. thesis, M.I.T., 1988.

[17] G. Sacchi Landriani, Spectral tau approximation of the two-dimensional Stokes problem. Numer. Math., 52 (1988), pp. 683-699. | MR | Zbl

[18] L. R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. Math. Modelling Num. Anal., 19 (1985), pp. 111-143. | Numdam | MR | Zbl

[19] L. R. Scott and M. Vogelius, Conforming Finite Element Methods for incompressible and nearly incompressible continua. Lectures in Applied Mathematics, 22, pp. 221-244, AMS, 1985. | MR | Zbl

[20] M. Suri, On the stability and convergence of higher order mixed finite element methods for second order elliptic problems. Math. Comput., 54 (1990), pp. 1-19. | MR | Zbl

[21] B. A. Szabo , I. Babuška and B. K. Chayapathy, Stress computations for nearly incompressible materials. Int. J. Numer. Methods Eng., 28 (1990), pp. 2175-2190. | Zbl

[22] R. Verführt, Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO, Numer. Anal., 18 (1984), pp 175-182. | Numdam | MR | Zbl

[23] M. Vogelius, An analysis of the p-Version of the Finite Element Method for nearly incompressible materials. Uniformly valid, optimal error estimates. Numerische Mathematik, 41 (1983), pp. 39-53. | MR | Zbl

[24] M. Vogelius, A right inverse for the divergence operator in spaces of piecewise polynomials. Application to the p-Version of the Finite Element Method. Numerische Mathematik, 41 (1983), pp. 19-37. | MR | Zbl

[25] C. Bernardi, Y. Maday and B. Metivet, Spectral approximation of the periodic-nonperiodic Navier-Stokes equations. Numerische Mathematik, 51 (1987), pp. 655-700. | MR | Zbl

[26] C. Bernardi, Y. Maday and B. Metivet, Calcul de la pression dans la résolution spectrale du problème de Stokes. La Recherche Aérospatiale, 1 (1987), pp. 1-21. | MR | Zbl

[27] M. Suri, The p-version of the finite element method for elliptic equations of order 2 l. M2AN, 24 (1990), pp. 265-304. | Numdam | MR | Zbl