Multistep-Galerkin Methods for Hyperbolic Equations
- 1 April 1979
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 33 (146) , 563-584
- https://doi.org/10.2307/2006297
Abstract
Multistep methods for first- and second-order ordinary differential equations are used for the full discretizations of standard Galerkin approximations to the initial-periodic boundary value problem for first-order linear hyperbolic equations in one space dimension and to the initial-boundary value problem for second-order linear selfadjoint hyperbolic equations in many space dimensions. -error bounds of optimal order in space and time are achieved for large classes of such multistep methods.Keywords
This publication has 13 references indexed in Scilit:
- Explicit finite element schemes for first order symmetric hyperbolic systemsNumerische Mathematik, 1976
- Linear Multistep Methods and Galerkin Procedures for Initial Boundary Value ProblemsSIAM Journal on Numerical Analysis, 1976
- Projection Methods with Different Trial and Test SpacesMathematics of Computation, 1976
- A Finite Element Method for First Order Hyperbolic EquationsMathematics of Computation, 1975
- The Relative Efficiency of Finite Difference and Finite Element Methods. I: Hyperbolic Problems and SplinesSIAM Journal on Numerical Analysis, 1974
- Galerkin Methods for First Order Hyperbolics: An ExampleSIAM Journal on Numerical Analysis, 1973
- Finite element methods for symmetric hyperbolic equationsNumerische Mathematik, 1973
- Convergence estimates for semi-discrete galerkin methods for initial-value problemsPublished by Springer Nature ,1973
- On finite element approximations to time-dependent problemsNumerische Mathematik, 1972
- THE FINITE ELEMENT METHOD AND APPROXIMATION THEORY**The preparation of this paper was supported by the National Science Foundation (GP-13778) and by the Office of Naval Research.Published by Elsevier ,1971