Estimates away from a discontinuity for dissipative Galerkin methods for hyperbolic equations

Author:
William J. Layton

Journal:
Math. Comp. **36** (1981), 87-92

MSC:
Primary 65N30; Secondary 65M15

DOI:
https://doi.org/10.1090/S0025-5718-1981-0595043-8

MathSciNet review:
595043

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Abstract: We consider the approximate solution of the initial value problem

*v*is taken to have a jump discontinuity at zero, that discontinuity will propagate along , in the true solution

*u*. Estimates in and of the pollution effects of the discontinuity are found. These estimates show those effects to decay exponentially in in regions a fixed distance

*d*from the discontinuity and exponentially in

*d*for fixed

*h*.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0595043-8

Article copyright:
© Copyright 1981
American Mathematical Society