×

Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems. (English) Zbl 0382.65056


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Jones, E., A generalization of the direct-stiffness method of structural analysis, Aiaa j., 2, 821-826, (1964) · Zbl 0119.19304
[2] Pian, T.H.H., Element stiffness matrices for boundary compatibility and for prescribed boundary stresses, (), 457-477
[3] Pian, T.H.H.; Tong, P., Basis of finite element methods for solid continua, Int. J. numer. meths. eng., 1, 3-85, (1969) · Zbl 0167.52805
[4] Tong, P., New displacement hybrid finite element models for solid continua, Int. J. numer. meths. eng., 2, 73-85, (1970) · Zbl 0247.73085
[5] Raviart, P.A., Hybrid finite element methods for solving 2nd order elliptic equations, () · Zbl 0339.65061
[6] Raviart, P.A.; Thomas, J.M., Primal hybrid finite element methods for 2nd order elliptic equations, () · Zbl 0364.65082
[7] Thomas, J.M., Méthodes des éléments finis hybrides duaux pour LES problèmes elliptiques du second-ordre, ()
[8] Yamamoto, Y., A formulation of matrix displacement method, ()
[9] Brezzi, F., Sur la méthode des éléments finis hybrides pour le problème biharmonique, Numer. math., 24, 103-131, (1975) · Zbl 0316.65029
[10] Brezzi, F.; Marini, L.D., On the numerical solution of plate bending problems by hybrid methods, RAIRO report, (1975) · Zbl 0322.73048
[11] de Veubeke, B.Fraeijs, Variational principles and the patch test, Int. J. numer. meths. eng., 8, 783-801, (1974) · Zbl 0284.73043
[12] Herrmann, L., Finite element bending analysis for plates, J. eng. mech. div. ASCE, 93, 000-000, (1967)
[13] Oden, J.T.; Reddy, J.N., On mixed finite element approximations, SIAM J. numer. anal., 13, 392-404, (1976) · Zbl 0337.65056
[14] Reddy, J.N.; Oden, J.T., Mathematical theory of mixed finite element approximations, Q. appl. math., 33, 255-280, (1975) · Zbl 0321.65057
[15] Ciarlet, P.G.; Raviart, P.A., A mixed finite element method for the biharmonic equation, (), 125-145 · Zbl 0337.65058
[16] Johnson, C., On the convergence of a mixed finite-element method for plate bending problems, Numer. math., 21, 43-62, (1973) · Zbl 0264.65070
[17] Nitsche, J., Convergence of nonconforming methods, (), 15-53
[18] Babuska, I.; Zlamal, M., Nonconforming elements in the finite element method, () · Zbl 0237.65066
[19] Miyoshi, T., Convergence of finite element solutions represented by a non-conforming basis, Kumamoto J. sci. math., 9, 11-20, (1972) · Zbl 0236.65071
[20] Strang, G., Variational crimes in the finite element method, (), 689-710
[21] Atluri, S., A new assumed stress hybrid finite element model for solid continua, Aiaa j., 9, 1647-1649, (1971) · Zbl 0231.73031
[22] Wolf, J.P., Generalized hybrid stress finite element models, Aiaa j., 11, 386-388, (1973)
[23] Wolf, J.P., Generalized stress models for finite element analysis, ()
[24] Agmon, S., Lectures on elliptic boundary value problems, (1965), Van Nostrand · Zbl 0151.20203
[25] Babuska, I., The finite element method with Lagrange multipliers, Numer. math., 20, 172-192, (1973)
[26] Babuska, I., Error bounds for finite element method, Numer. meth., 16, 322-333, (1971) · Zbl 0214.42001
[27] Babuska, I.; Aziz, A.K., Survey lectures on the mathematical theory of finite elements, (), 3-359
[28] Oden, J.T.; Reddy, J.N., An introduction to the mathematical theory of finite elements, (1976), Wiley Interscience New York · Zbl 0336.35001
[29] Lee, J.K., Convergence of mixed-hybrid finite element methods, ()
[30] Rachford, H.H.; Wheeler, M.F., An H-1-Galerkin procedure for the two-point boundary-value problem, (), 353-382
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.