ISSN:
1572-9125
Keywords:
Hyperbolic conservation laws
;
two space dimensions
;
relaxation terms
;
non-equilibrium
;
error estimate
;
rate of convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order $$\mathcal{O}(\sqrt {\Delta t} )$$ measured inL 1 is derived. This error bound is independent of the relaxation time δ 〉 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured inL 1 is of order $$\mathcal{O}(\delta ^{1/3} )$$ . Finally, we present some numerical illustrations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01733792
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