The unconditional instability of inflow-dependent boundary conditions in difference approximations to hyperbolic systems

Author:
Eitan Tadmor

Journal:
Math. Comp. **41** (1983), 309-319

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717688-6

MathSciNet review:
717688

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Abstract: It is well known that for a mixed initial-boundary hyberbolic system to be well-defined it is necessary to impose *additional* boundary conditions only on the inflow eigenspace of the problem. We prove the discrete analogue of the above concerning difference approximations to such a system; that is, imposing numerical boundary conditions which are at least zeroth-order accurate with an *inflow* part of the interior equations leads to unconditional instability.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0717688-6

Article copyright:
© Copyright 1983
American Mathematical Society