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On finite element approximations to time-dependent problems. (English) Zbl 0244.65063

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
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References:
[1] Agmon, S.: Lectures on elliptic boundary value problems. Academic Press. · Zbl 0142.37401
[2] Aubin, J. P.: Approximation des espaces de distributions et des opérateurs différentiels. Bull. Soc. Math. France. Mémoire 12 (1967).
[3] Coddington Levinson: Ordinary differential equations. McGraw-Hill 1955.
[4] Descloux, J.: On the numerical integration of the heat equation. Numer. Math.15, 371-381 (1970). · Zbl 0211.19202
[5] Douglas, J., Dupont, T.: Galerkin methods for parabolic problems. SIAM J. Numer. Anal.7, 575-626 (1970). · Zbl 0224.35048
[6] Boor, C. de, Fix, G.: Approximation by spline quasi-interpolates. To appear. · Zbl 0279.41008
[7] Fix, G., Strang, G.: Fourier analysis of the finite element method. Studies in Applied Mathematics48, 265-273 (1969). · Zbl 0179.22501
[8] Kine, J. T.: Least squares methods for parabolic problems. To appear in SINUM.
[9] Lions, J. L.: Equations Différentielles Opérationelles. Springer 1961.
[10] Lions, J. L., Magènes, E.: Problèmes aux limites non homogènes et applications. Dunod 1969.
[11] Price, H. S., Varga, R. S.: Numerical analysis of simplified models of fluid flow in porous media. To appear.
[12] Showalter, R. E., Ting, T. W.: Pseudoparabolic differential equations. SIAM J. Math. Anal.1, 1-26 (1970). · Zbl 0199.42102
[13] Strang, G., Fix, G.: An analysis of the finite element method. Prentice-Hall, to appear. · Zbl 0356.65096
[14] Swartz, B., Wendroff, B.: Generalized finite-difference schemes. Math. of Comp.23, 37-50 (1969). · Zbl 0184.38502
[15] Varga, R. S.: Functional analysis and approximation theory, in numerical analysis. Proc. Regional Conference supported by the NSF at Boston University, July 20-24, 1970. · Zbl 0192.59101
[16] Birkhoff, G.: Spline approximation by moments. J. Math. Mech.16, 987-990 (1967); see also p. 209-210 of I. J. Schoenberg, ed., Approximations with special emphasis on spline functions. Academic Press 1970. · Zbl 0148.29204
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