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Delfour, M.; Hager, W.; Trochu, F.

Discontinuous Galerkin methods for ordinary differential equations. (English) Zbl 0469.65053

Math. Comput. 36, 455-473 (1981).
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Cited in 2 Reviews
Cited in 118 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations

Keywords:

Galerkin methods; discontinuous piecewise polynomial spaces; one-step schemes
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Full Text: DOI

References:

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[12] M. C. Delfour, The linear quadratic optimal control problem for hereditary differential systems: theory and numerical solution, Appl. Math. Optim. 3 (1976/77), no. 2/3, 101 – 162. · Zbl 0404.49010 · doi:10.1007/BF01441963
[13] M. C. Delfour & F. Dubeau, Piecewise Discontinuous Polynomial Approximation of Nonlinear Ordinary Differential Equations, Centre de Recherches Mathématiques, Université de Montréal, Report #865, 1979. · Zbl 0633.65068
[14] M. C. Delfour and F. Trochu, Discontinuous finite element methods for the approximation of optimal control problems governed by hereditary differential systems, Distributed parameter systems: modelling and identification (Proc. IFIP Working Conf., Rome, 1976) Springer, Berlin, 1978, pp. 256 – 271. Lecture Notes in Control and Informat. Sci., Vol. 1. · Zbl 0498.49017
[15] Michel Defour and François Trochu, Approximation des équations différentielles et problèmes de commande optimale, Ann. Sci. Math. Québec 1 (1977), no. 2, 211 – 225 (French). Compte Rendu du Deuxième Colloque CRM-IRIA (Centre Recherche Math., Univ. Montréal, Montreal, Que., 1976). · Zbl 0418.65035
[16] M. C. Delfour & F. Trochu, Discontinuous Approximation of Ordinary Differential Equations and Application to Optimal Control Problems, Centre de Recherches Mathématiques, Université de Montréal, Report #751, 1977. · Zbl 0418.65035
[17] Bernie L. Hulme, Discrete Galerkin and related one-step methods for ordinary differential equations, Math. Comp. 26 (1972), 881 – 891. · Zbl 0272.65056
[18] Bernie L. Hulme, One-step piecewise polynomial Galerkin methods for initial value problems, Math. Comp. 26 (1972), 415 – 426. · Zbl 0265.65038
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[23] L. C. Wellford Jr. and J. T. Oden, A theory of discontinuous finite element Galerkin approximations of shock waves in nonlinear elastic solids. I. Variational theory, Comput. Methods Appl. Mech. Engrg. 8 (1976), no. 1, 1 – 16. , https://doi.org/10.1016/0045-7825(76)90049-9 L. C. Wellford Jr. and J. T. Oden, A theory of discontinuous finite element Galerkin approximations of shock waves in nonlinear elastic solids. II. Accuracy and convergence, Comput. Methods Appl. Mech. Engrg. 8 (1976), no. 1, 17 – 36. · Zbl 0341.73043 · doi:10.1016/0045-7825(76)90050-5
[24] L. C. Wellford Jr. and J. T. Oden, A theory of discontinuous finite element Galerkin approximations of shock waves in nonlinear elastic solids. I. Variational theory, Comput. Methods Appl. Mech. Engrg. 8 (1976), no. 1, 1 – 16. , https://doi.org/10.1016/0045-7825(76)90049-9 L. C. Wellford Jr. and J. T. Oden, A theory of discontinuous finite element Galerkin approximations of shock waves in nonlinear elastic solids. II. Accuracy and convergence, Comput. Methods Appl. Mech. Engrg. 8 (1976), no. 1, 17 – 36. · Zbl 0341.73043 · doi:10.1016/0045-7825(76)90050-5
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