Continuous finite elements in space and time for the heat equation

On analyse une nouvelle methode variationnelle pour l'approximation de l'equation de la chaleur a l'aide des elements finis continus dans l'espace et le temps. On presente les estimations d'erreurs et les resultats d'experiences numeriques

[1]  B. Hulme.  Discrete Galerkin and related one-step methods for ordinary differential equations , 1972 .

[2]  Vidar Thomée,et al.  Negative norm estimates and superconvergence in Galerkin methods for parabolic problems , 1980 .

[3]  Claes Johnson,et al.  Error estimates and automatic time step control for nonlinear parabolic problems, I , 1987 .

[4]  R. S. Falk,et al.  Analysis of a continuous finite element method for hyperbolic equations , 1987 .

[5]  P. Lesaint,et al.  Finite element collocation methods for first-order systems , 1979 .

[6]  Pierre Jamet,et al.  Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain , 1977 .

[7]  M. Wheeler.  A Priori L_2 Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations , 1973 .

[8]  R. Rannacher,et al.  On the Smoothing Property of the Galerkin Method for Parabolic Equations , 1982 .

[9]  B. Hulme.  One-step piecewise polynomial Galerkin methods for initial value problems , 1972 .

[10]  Kenneth Eriksson,et al.  Time discretization of parabolic problems by the discontinuous Galerkin method , 1985 .

[11]  Jim Douglas,et al.  Collocation Methods for Parabolic Equations in a Single Space Variable , 1974 .

[12]  Pierre Jamet.  Stability and Convergence of a Generalized Crank-Nicolson Scheme on a Variable Mesh for the Heat Equation , 1980 .

[13]  Philippe G. Ciarlet,et al.  The Finite Element Method for Elliptic Problems. , 1981 .

[14]  M. Nikolskii,et al.  Approximation of Functions of Several Variables and Embedding Theorems , 1971 .

[15]  Mary F. Wheeler,et al.  A Quasi-Projection Analysis of Galerkin Methods for Parabolic and Hyperbolic Equations , 1978 .

[16]  Ragnar Winther.  A stable finite element method for initial-boundary value problems for first-order hyperbolic systems , 1981 .

[17]  O. Ladyženskaja.  Linear and Quasilinear Equations of Parabolic Type , 1968 .