On the stability of Galerkin methods for initial-boundary value problems for hyperbolic systems
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- by Max D. Gunzburger PDF
- Math. Comp. 31 (1977), 661-675 Request permission
Abstract:
The stability of approximating the solution of mixed initial-boundary value problems for hyperbolic systems by semidiscrete Galerkin methods is studied. It is shown that a particular straightforward Galerkin method yields an unstable approximation, and that this numerical instability is caused by an improper treatment of the boundary. Stable schemes are then presented, one of which differs from the unstable scheme only insofar as the treatment of the boundary is concerned. These stable schemes make use of a particular matrix which symmetrizes the differential system. It is therefore shown that the use of this matrix is crucial to the stability of the computations as well as for obtaining a priori bounds on the energy of the continuous system. This symmetrizing matrix is also related to the diagonalizing matrix for the system of hyperbolic equations and to the Lyapunov matrix for the system of ordinary differential equations resulting from the application of Galerkin’s method.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 661-675
- MSC: Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-1977-0436624-0
- MathSciNet review: 0436624