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A quasi-projection analysis of Galerkin methods for parabolic and hyperbolic equations. (English) Zbl 0385.65052


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
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[1] Jim Douglas Jr. and Todd Dupont, Galerkin approximations for the two point boundary problem using continuous, piecewise polynomial spaces, Numer. Math. 22 (1974), 99 – 109. · Zbl 0331.65051
[2] Jim Douglas Jr. and Todd Dupont, Collocation methods for parabolic equations in a single space variable, Lecture Notes in Mathematics, Vol. 385, Springer-Verlag, Berlin-New York, 1974. Based on \?\textonesuperior -piecewise-polynomial spaces. · Zbl 0279.65097
[3] J. DOUGLAS, JR., T. DUPONT & M. F. WHEELER, A Quasi-Projection Approximation Method Applied to Galerkin Procedures for Parabolic and Hyperbolic Equations, Math. Res. Center Rep. #1465, 1974.
[4] Jim Douglas Jr., Todd Dupont, and Mary Fanett Wheeler, A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary value problems, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974), no. R-2, 47 – 59 (English, with Loose French summary). · Zbl 0315.65063
[5] Jim Douglas Jr., Todd Dupont, and Mary Fanett Wheeler, Some superconvergence results for an \?\textonesuperior -Galerkin procedure for the heat equation, Computing methods in applied sciences and engineering (Proc. Internat. Sympos., Versailles, 1973) Springer, Berlin, 1974, pp. 288 – 311. Lecture Notes in Comput. Sci., Vol. 10.
[6] Todd Dupont, Some \?² error estimates for parabolic Galerkin methods, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 491 – 504.
[7] H. H. Rachford Jr., Two-level discrete-time Galerkin approximations for second order nonlinear parabolic partial differential equations, SIAM J. Numer. Anal. 10 (1973), 1010 – 1026. · Zbl 0239.65086
[8] J. A. WHEELER, Simulation of Heat Transfer From a Warm Pipeline Buried in Permafrost, presented to the 74th National Meeting of the American Institute of Chemical Engineers, New Orleans, March, 1973.
[9] 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
[10] Mary Fanett Wheeler, \?_{\infty } estimates of optimal orders for Galerkin methods for one-dimensional second order parabolic and hyperbolic equations, SIAM J. Numer. Anal. 10 (1973), 908 – 913. · Zbl 0266.65074
[11] Mary Fanett Wheeler, A Galerkin procedure for estimating the flux for two-point boundary value problems, SIAM J. Numer. Anal. 11 (1974), 764 – 768. · Zbl 0292.65046
[12] Mary F. Wheeler, An \?\(^{-}\)\textonesuperior Galerkin method for parabolic problems in a single space variable, SIAM J. Numer. Anal. 12 (1975), no. 5, 803 – 817. · Zbl 0331.65075
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