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Galerkin-Runge-Kutta methods and hyperbolic initial boundary value problems. (English) Zbl 0348.65087

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
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References:
[1] Agmon, S.: Elliptic Boundary Value Problems. New York: Van Nostrand 1965. · Zbl 0142.37401
[2] Gekeler, E.: Linear multistep methods and Galerkin procedures for initial boundary value problems. (To appear in SINUM.) · Zbl 0335.65042
[3] Grigorieff, R. D.: Numerik gewöhnlicher Differentialgleichungen. Stuttgart: I. Teubner 1972. · Zbl 0249.65051
[4] Schutlz, M. H.:L 2 error bounds for the Rayleight-Ritz-Galerkin method. SINUM8, 737–748 (1971). · Zbl 0285.65070
[5] Strang, G., Fix, G. J.: An Analysis of the Finite Element Method. Englewood Cliffs, N. J.: Prentice-Hall 1973. · Zbl 0356.65096
[6] Thomée, V.: Some convergence results for Galerkin methods for parabolic boundary value problems. In: Mathematical Aspects of the Finite Elements in Partial Differential Equations, Proc. of a Symposium of the MRC Wisconsin, Madison 1974. New York: Academic Press 1974.
[7] Zlamal, M.: Curved elements in the finite element method I. SINUM10, 229–240 (1973). · Zbl 0285.65067
[8] Zlamal, M.: Curved elements in the finite element method II. SINUM11, 347–362 (1974). · Zbl 0277.65064
[9] Zlamal, M.: Unconditionally stable finite element schemes for parabolic equations. In: Topics in Numerical Analysis II (Miller, J. H., ed.). London: Academic Press 1974. · Zbl 0296.65054
[10] Zlamal, M.: Finite element multistep discretizations of parabolic boundary value problems. Mathem. Computation29, 350–359 (1975). · Zbl 0302.65081 · doi:10.2307/2005556
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