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


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
Full Text: DOI EuDML


[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 · doi:10.1007/BF02165508
[5] Douglas, J., Dupont, T.: Galerkin methods for parabolic problems. SIAM J. Numer. Anal.7, 575-626 (1970). · Zbl 0224.35048 · doi:10.1137/0707048
[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 · doi:10.1137/0501001
[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 · doi:10.1090/S0025-5718-1969-0239768-7
[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
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.