Convergence of MUSCL Relaxing Schemes to the Relaxed Schemes for Conservation Laws with Stiff Source Terms |
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| Authors: | Tao Tang Jinghua Wang |
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| Affiliation: | (1) Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA;(2) Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA 94305, USA |
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| Abstract: | We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l
1- and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter  , the Lipschitz constant of the stiff source term and the time step  t. The Lipschitz constant of the l
1 continuity in time for the MUSCL relaxing schemes is shown to be independent of and t. The convergence of the relaxing schemes to the corresponding MUSCL relaxed schemes is then established. |
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| Keywords: | relaxation scheme nonlinear conservation laws maximum principle convergence |
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