Nédélec, J. C. A new family of mixed finite elements in \({\mathbb{R}}^ 3\). (English) Zbl 0625.65107 Numer. Math. 50, 57-81 (1986). The objective of this paper is to present two families of mixed finite elements in three dimensions. Both families are conforming, the first one in H(div) and the second in H(curl), and both are split in three, corresponding to the case of tetrahedrons, cubes and prisms. The author describes these elements, proves the unisolvance and estimates the interpolation error. Finally these elements are used to approximate the Stokes’ system. Reviewer: C.-I.Gheorghiu Cited in 7 ReviewsCited in 467 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 76D07 Stokes and related (Oseen, etc.) flows 35J25 Boundary value problems for second-order elliptic equations Keywords:space H(div), space H(curl); conforming finite elements family; mixed finite elements; Stokes’ system × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Brezzi, F.: On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO8, 129-151 (1974) · Zbl 0338.90047 [2] Brezzi, F., Douglas, J., Marini, L.D.: Two families of mixed finite elements for second order elliptic problems. (To appear in Numer. Math.) · Zbl 0599.65072 [3] Ciarlet, P.G.: The finite element method for elliptic problems, Amsterdam North Holland 1978 · Zbl 0383.65058 [4] Ciarlet, P.G., Raviart, P.A.: A mixed finite element method for the biharmonic equation. Mathématical aspects in finite element method (C. de Boor ed.), pp. 125-145. New York: Academic Press 1974 · Zbl 0337.65058 [5] Fortin, M.: An analysis of the convergence of mixed finite element method. RAIRO11, 341-354 (1977) · Zbl 0373.65055 [6] Nédélec, J.C.: Mixed finite element in ?3. Numer. Math.35, 315-341 (1980) · Zbl 0419.65069 · doi:10.1007/BF01396415 [7] Nédélec, J.C.: Elements finis mixtes incompressibles pour l’equation de Stokes dans ?3. Numer. Math.39, 97-112 (1982) · Zbl 0488.76038 · doi:10.1007/BF01399314 [8] Raviart, P.A., Thomas, J.M.: A mixed finite element method for 2nd order elliptic problems. In: Mathematical aspects of finite element methods (A. Dold and B. Eckmann, eds.) Lect. Notes 606. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0362.65089 [9] Thomas, J.M.: Thesis Paris (1977) 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.