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Interpolation theory over curved elements, with applications to finite element methods. (English) Zbl 0261.65079

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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[1] Argyris, J.H.; Argyris, J.H.; Argyris, J.H.; Argyris, J.H.; Argyris, J.H.; Argyris, J.H., Energy theorems and structural analysis, part I: general theory, Aircraft engineering, Aircraft engineering, Aircraft engineering, Aircraft engineering, Aircraft engineering, Aircraft engineering, 27, 125-134, (1955) · Zbl 0161.21601
[2] Also published as book (Butterworths Scientific Publications, London, 4th reprint 1971).
[3] Argyris, J.H.; Fried, I., The LUMINA element for the matrix displacement method (Lagrangian interpolation), The aeronautical journal of the royal aeronautical society, 72, 514-517, (1968)
[4] Argyris, J.H.; Scharpf, D.W., The HERMES 8 element for the matrix displacement method (Hermitian interpolation), The aeronautical journal of the royal aeronautical society, 72, 613-617, (1968)
[5] Argyris, J.H.; Scharpf, D.W., The curved tetrahedronal and triangular elements TEC and TRIG for the matrix displacement method, part I: small displacements, part II: large displacements, The aeronautical journal of the royal aeronautical society, 73, 55-65, (1969)
[6] Nečas, J., LES méthodes directes en théorie des équations elliptiques, (1967), Masson Paris · Zbl 1225.35003
[7] Zienkiewicz, O.C., The finite element method in engineering science, (1971), McGraw-Hill London · Zbl 0237.73071
[8] Argyris, J.H.; Balmer, H.; Doltsinis, J.; Willam, K., Finite element analysis of thermomechanical problems, (), To be published in Proceedings. · Zbl 0435.73086
[9] Ergatoudis, I.; Irons, B.M.; Zienkiewicz, O.C., Curved, isoparametric, “quadrilateral” elements for finite element analysis, Int. J. solids structures, 4, 31-42, (1968) · Zbl 0152.42802
[10] Strang, G.; Berger, A.E., The change in solution due to change in domain, (1971), Private communication
[11] Fried, I., Discretization and round-off errors in the finite element analysis of elliptic boundary value problems and eigen-value problems, ()
[12] M.Zlámal, Curved elements in the finite element method,.to be published.
[13] M.Zlámal, The finite element method in domains with curved boundaries, to be published.
[14] P.G.Ciarlet and P.-A.Raviart, General Lagrange and Hermite interpolation in Rn with applications to finite element methods, Arch. Rational Mech. Anal. To be published. · Zbl 0243.41004
[15] Bramble, J.H.; Hilbert, S.R., Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. math., 16, 362-369, (1971) · Zbl 0214.41405
[16] Cartan, H., Calcul différentiel, (1967), Hermann Paris · Zbl 0156.36102
[17] Ciarlet, P.G.; Wagschal, C., Multipoint Taylor formulas and applications to the finite element method, Numer. math., 17, 84-100, (1971) · Zbl 0199.50104
[18] Argyris, J.H., Some results on the free-free oscillations of aircraft type structures, (), Also · Zbl 0251.73030
[19] Argyris, J.H., Continua and discontinua, (), 1-198, published in the Proceedings of the Conference by United States Government
[20] Felippa, C.A.; Clough, R.W., The finite element method in solid mechanics, (), 210-252, SIAM-AMS Proceedings II
[21] Nachbin, L., Topology on spaces of holomorphic mappings, (1969), Springer-Verlag Berlin · Zbl 0172.39902
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