Stability of interfaces with mesh refinement

Author:
Marsha J. Berger

Journal:
Math. Comp. **45** (1985), 301-318

MSC:
Primary 65M10; Secondary 65M50

DOI:
https://doi.org/10.1090/S0025-5718-1985-0804925-4

MathSciNet review:
804925

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Abstract: We study the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, we derive a root condition which implies stability for the initial-boundary value problem for this type of interface. From the root condition, we prove the stability of several interface equations using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, we prove stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap.

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0804925-4

Article copyright:
© Copyright 1985
American Mathematical Society