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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 595043
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Abstract: We consider the approximate solution of the initial value problem

$\displaystyle \frac{{\partial u}}{{\partial t}} = \frac{{\partial u}}{{\partial x}},\quad u(x,0) = v(x),$

by a dissipative Galerkin method. When v is taken to have a jump discontinuity at zero, that discontinuity will propagate along $ x + t = 0$, in the true solution u. Estimates in $ {L_2}$ and $ {L_\infty }$ of the pollution effects of the discontinuity are found. These estimates show those effects to decay exponentially in $ {h^{ - 1}}$ in regions a fixed distance d from the discontinuity and exponentially in d for fixed h.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0595043-8
PII: S 0025-5718(1981)0595043-8
Article copyright: © Copyright 1981 American Mathematical Society