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Single step Galerkin approximations for parabolic problems. (English) Zbl 0378.65061

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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[8] Hans-Peter Helfrich, Fehlerabschätzungen für das Galerkinverfahren zur Lösung von Evolutionsgleichungen, Manuscripta Math. 13 (1974), 219 – 235 (German, with English summary). · Zbl 0323.65037 · doi:10.1007/BF01168227 · doi.org
[9] G. J. Makinson, Stable high order implicit methods for the numerical solution of systems of differential equations, Comput. J. 11 (1968/1969), 305 – 310. · Zbl 0167.15704 · doi:10.1093/comjnl/11.3.305 · doi.org
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[12] Vidar Thomée, Some convergence results for Galerkin methods for parabolic boundary value problems, Mathematical aspects of finite elements in partial differential equations (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1974), Math. Res. Center, Univ. of Wisconsin-Madison, Academic Press, New York, 1974, pp. 55 – 88. Publication No. 33.
[13] Vidar Thomée, High order local approximations to derivatives in the finite element method, Math. Comp. 31 (1977), no. 139, 652 – 660. · Zbl 0367.65055
[14] Mary Fanett Wheeler, A priori \?\(_{2}\) error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal. 10 (1973), 723 – 759. · Zbl 0232.35060 · doi:10.1137/0710062 · doi.org
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