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.
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This research has been supported by the Norwegian Research Council (NFR), program no. STP 110673/420, at the Department of Applied Mathematics, SINTEF, Oslo, Norway
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Shen, W., Tveito, A. & Winther, R. A system of conservation laws including a stiff relaxation term; the 2D case. Bit Numer Math 36, 786–813 (1996). https://doi.org/10.1007/BF01733792
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DOI: https://doi.org/10.1007/BF01733792