no. 1
Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
ESAIM: Modélisation mathématique et analyse numérique, Tome 19 (1985) no. 1, pp. 111-143. 
@article{M2AN_1985__19_1_111_0,
     author = {Scott, L. R. and Vogelius, M.},
     title = {Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {111--143},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {19},
     number = {1},
     year = {1985},
     mrnumber = {813691},
     zbl = {0608.65013},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1985__19_1_111_0/}
}
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Scott, L. R.; Vogelius, M. Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. ESAIM: Modélisation mathématique et analyse numérique, Tome 19 (1985) no. 1, pp. 111-143. http://archive.numdam.org/item/M2AN_1985__19_1_111_0/

[1] D. N. Arnold, L. R. Scott, M. Vogelius, Regular solutions of div u = f with Dirichlet boundary conditions on a polygon, Tech. Note, University of Maryland, to appear.

[2] I. Babuska, K. Aziz, Survey lectures on the mathematical foundations of the finite element method. In The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A. K. Aziz, editor, Academic Press, 1972. | MR | Zbl

[3] J. M. Boland, R.A. Nicolaides, Stability of finite elements under devergence constraints, SIAM J. Num. Anal. 20 (1983), pp. 722-731. | MR | Zbl

[4] M. Crouzeix, P. A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations, I. R.A.LR.O. Sér. Rouge 7 (1973), pp. 33-75. | Numdam | MR | Zbl

[5] P.C. Dunne, Reply to comments by B. Irons on his paper « Complete polynomial displacement fields for finite element method », Aero. J. Roy. Aero. Soc.72 (1973) pp. 710-711.

[6] G. J. Fix, M. D. Gunzburger, R. A. Nicolaides, On mixed finite element methods for first order elliptic systems. Numer. Math. 37 (1981), pp. 29-48. | MR | Zbl

[7] V. Girault, P. A. Raviart, Finite Element Approximation of the Navier-Stokes Equation. Lecture Notes in Mathematics, 749, Springer-Verlag, 1979. | MR | Zbl

[8] P. Grisvard, Boundary value problems in non-smooth domains, Lecture Notes # 19, University of Maryland, 1980.

[9] B. Mercier, A conforming finite element method for two dimensional, incompressible elasticity, Int. J. Num Meths. Eng. 14 (1979), pp. 942-945. | MR | Zbl

[10] J. Morgan R. Scott, A nodal basis for C 1 piecewise polynomials of degree n≥5 no 5. Math. Comput. 29 (1975), pp. 736-740. | MR | Zbl

[11] J. MorganR. Scott, The dimension of the space of C 1 piecewise polynomials (Preprint).

[12] L. R. Scott, M. Vogelius, Conforming finite element methods for incompressible and nearly incompressible continua. Proceedings of the 1983 Summer Seminar on Large-scale Computations in Fluid Mechanics, S. Osher, editor, Lect. Appl. Math. 22, to appear. | MR | Zbl

[13] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. | MR | Zbl

[14] R. Stenberg, Analysis of mixed finite element methods for the Stokes problem : A unified approach. To appear, Math. Comp. | MR | Zbl

[15] G. Strang, Piecewise polynomials and the finite element method, Bull. AMS 79 (1973), pp, 1128-1137. | MR | Zbl

[16] B. A. Szabo, P. K. Basu, D. A. Dunavant, D. Vasilopoulos, Adaptive finite element technology in integrated design and analysis, Report WU/CCM-81/1. Washington Univestity, St. Louis.

[17] R. Temam, Navier-Stokes Equations, North-Holland, 1977. | MR | Zbl

[18] M. Vogelius, A right-inverse for the divergence operator in spaces of piecewise polynomials. Application to the p-version of the finite element method. Numer. Math. 41 (1983), pp. 19-37. | MR | Zbl

[19] M. Vogelius, An analysis of thep-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal error estimates. Numer. Math. 41 (1983), pp. 39-53. | MR | Zbl