Vogelius, Michael 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 Numer. Math. 41, 19-37 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 41 Documents MSC: 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 Keywords:divergence operator; maximal right-inverse; finite element method; optimal convergence; Laplace equation; Stokes problem × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [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 · doi:10.1007/BF01398256 [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 · doi:10.1007/BF01399326 [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 · doi:10.1137/0718033 [5] Bellman, R.: A note on an inequality of E. Schmidt. Bull. A.M.S.50, 734-737 (1944) · Zbl 0061.10402 · doi:10.1090/S0002-9904-1944-08228-1 [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 · doi:10.1090/S0025-5718-1976-0403260-0 [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 · doi:10.1007/BF01396185 [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 · doi:10.1016/0898-1221(78)90021-4 [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 · doi:10.1007/BF01396304 [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 · doi:10.1137/0142091 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.