Anti-Dissipative Schemes for Advection and Application to Hamilton–Jacobi–Bellmann Equations |
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| Authors: | Olivier Bokanowski Hasnaa Zidani |
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| Affiliation: | (1) Lab. Jacques-Louis Lions, Université Pierre et Marie Curie, 175 Rue Chevaleret, Paris, 75013, France;(2) ENSTA, UMA, 32 Boulevard Victor, Paris Cedex 15, 75739, France |
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| Abstract: | We propose two new antidiffusive schemes for advection (or linear transport), one of them being a mixture of Roe’s Super-Bee scheme and of the “Ultra-Bee” scheme. We show how to apply these schemes to treat time-dependent first order Hamilton–Jacobi–Bellman equations with discontinuous initial data, possibly infinitely-valued. Numerical tests are proposed, in one and two space dimensions, in order to validate the methods AMS subject classifications. Primary 65M12, Secondary 58J47 |
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| Keywords: | Advection equation antidiffusive scheme Ultra-Bee limiter Super-Bee limiter Hamilton– Jacobi– Bellman equation |
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