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Approximation in the finite element method. (English) Zbl 0221.65174

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
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References:
[1] Bramble, J.: Variational methods for the numerical solution of linear problems. Lecture notes, Chalmers Inst. of Techn., 1970.
[2] Bramble, J., Hilbert, S. H.: Estimation of linear functionals on Sobolev spaces. SIAM Num. Anal.7, 112-124 (1970). · Zbl 0201.07803 · doi:10.1137/0707006
[3] Bramble, J., Hilbert, S. H.: Bounds for a class of linear functionals with applications to Hermite interpolation. Num. Math.16, 362-369 (1971). · Zbl 0214.41405 · doi:10.1007/BF02165007
[4] Bramble, J., Zlámal, M.: Triangular elements in the finite element method. Math. Comp.24, 809-820 (1970). · Zbl 0226.65073 · doi:10.1090/S0025-5718-1970-0282540-0
[5] Ciarlet, P., Raviart, P.: General Lagrange and Hermite interpolation inR n with applications to finite element methods. Arch. Rat. Mech. Anal., to appear. · Zbl 0243.41004
[6] Ne?as, J.: Les méthodes directes en théorie des équations elliptiques. Paris: Masson 1967.
[7] Nitsche, J.: Ein Kriterium für die quasi-Optimalität des Ritzschen Verfahrens. Num. Math.11, 346-348 (1968). · Zbl 0175.45801 · doi:10.1007/BF02166687
[8] Nitsche, J.: A projection method for Dirichlet problems using subspaces with nearly zero boundary conditions. Unpublished manuscript. · Zbl 0271.65059
[9] Strang, G.: The finite element method and approximation theory. Numerical solutions of partial differential equations II (SYNSPADE), ed. by Hubbard. New York: Academic Press 1971.
[10] Strang, G., Berger, A.: The change in solution due to change in domain. Unpublished manuscript, submitted to Proceedings of the A.M.S. Summer Institute on Partial Differential Equations, Berkeley, 1971. · Zbl 0259.35020
[11] Strang, G., Fix, G.: An analysis of the finite element method. To be published by Prentice-Hall. · Zbl 0356.65096
[12] ?eni?ek, A.: Konvergence methody Kone?ných prvk? pro okrajove problemy Systému eliptických rovnic. Apl. Matem.14, 355-377 (1969).
[13] Zienkiewicz, O. C., Cheung, Y. K.: The finite element method in structural and continum mechanics. New York: McGraw-Hill 1967. · Zbl 0189.24902
[14] Zlámal, M.: On the finite element method. Num. Math.12, 394-409 (1968). · Zbl 0176.16001 · doi:10.1007/BF02161362
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