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A right-inverse for divergence operator in spaces of piecewise polynomials. Application to the p-version of the finite element method. (English) Zbl 0504.65060

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
76D07 Stokes and related (Oseen, etc.) flows
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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[1] Babuska, I., Dorr, M.: Error estimates for the combinedh-andp-versions of the finite element method. Numer. Math.37, 257-277 (1981) · Zbl 0487.65058
[2] Babuska, I., Kellogg, R.B., Pitkäranta, J.: Direct and inverse error estimates for finite elements with mesh refinements. Numer. Math.33, 447-471 (1979) · Zbl 0423.65057
[3] Babuska, I., Szabo, B.A.: On the rates of convergence of the finite element method. Report WU/CCM-80/2. St. Louis: WashingtonUniversity. Internat. J. Numer. Meth. Engng. (To appear)
[4] Babuska, I., Szabo, B.A., Katz, I.N.: Thep-version of the finite element method. SIAM J. Numer. Anal.18, 515-545 (1981) · Zbl 0487.65059
[5] Bellman, R.: A note on an inequality of E. Schmidt. Bull. A.M.S.50, 734-737 (1944) · Zbl 0061.10402
[6] Bergh, J., Lösttröm, J.: Interpolation Spaces. Berlin, Heidelberg, New York: Springer, 1976 · Zbl 0344.46071
[7] Crouzeix, M., Raviart, P.A.: Confirming and nonconfirming finite element methods for solving the stationary Stokes equations I. Rev. Francaise Automat. Informat. Recherche Opèrationnelle Sèr. Rouge7, 33-75 (1973)
[8] Falk, R.S.: An analysis of the finite element method using Lagrange multipliers for the stationary Stokes equations. Math. Comput.30, 241-249 (1976) · Zbl 0351.65028
[9] Falk, R.S.: A finite element method for the stationary Stokes equations using trial functions which do not have to satisfy divv=0. Math. Comput.30, 698-702 (1976) · Zbl 0368.35026
[10] Fix, G.J., Gunzburger, M.D., Nicolaides, R.A.: On mixed finite element methods for first order elliptic systems. Numer. Math.37, 29-48 (1981) · Zbl 0459.65072
[11] Katz, I.N., Peano, A.G., Rossow, M.P.: Nodal variables for complete confirming finite elements of arbitrary polynomial order. Comput. Math. Appl.4, 85-112 (1978) · Zbl 0402.73068
[12] Morgan, J., Scott, R.: A nodal basis forC 1 piecewise polynomials of degree >=5. Math. Comput.29, 736-740 (1975) · Zbl 0307.65074
[13] Raviart, P.A., Thomas, J.M.: A mixed finite element method for 2-nd order elliptic problems, pp. 292-315. In: Mathematical Aspects of Finite Element Methods. (eds.) Galligani, I., Magenes, E. Springer Lecture Notes in Math.606, 1975
[14] Temam, R.: Navier-Stokes Equations. North-Holland, 1977 · Zbl 0383.35057
[15] Vogelius, M.: An analysis of thep-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal error estimates. Numer. Math.41, 39-53 (1983) · Zbl 0504.65061
[16] Vogelius, M., Papanicolaou, G.: A projection method applied to diffusion in a periodic structure. SIAM J. Appl. Math.42, 1307-1327 (1982) · Zbl 0519.35001
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