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Convergence of an Antidiffusion Lagrange-Euler Scheme for Quasilinear Equations
This paper presents an explicit scheme which may be broken into several steps. The first one is a transport phase for a time step, with a projection on a Lagrangian mesh. Then a new projection is performed on a fixed Eulerian mesh. Lastly a corrected antidiffusion step of the SHASTA type occurs. A s...
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| Published in: | SIAM journal on numerical analysis 1984-10, Vol.21 (5), p.985-994 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c971-c9643dec38770d161a1d4a3c427c1e7b6ca99d1066d9dc9142c144f563838b183 |
| container_end_page | 994 |
| container_issue | 5 |
| container_start_page | 985 |
| container_title | SIAM journal on numerical analysis |
| container_volume | 21 |
| creator | Le Roux, A. Y. Quesseveur, P. |
| description | This paper presents an explicit scheme which may be broken into several steps. The first one is a transport phase for a time step, with a projection on a Lagrangian mesh. Then a new projection is performed on a fixed Eulerian mesh. Lastly a corrected antidiffusion step of the SHASTA type occurs. A stability condition appears to make the scheme easily computable. This condition allows larger timesteps than the well known Courant-Friedrichs-Lewy condition. A more complex version of the scheme is proposed, which works without any stability condition. Convergence towards the entropy solution is proved. A few numerical experiments are reported, showing the quality of the approximation of shocks or giving some information about the precision. |
| doi_str_mv | 10.1137/0721061 |
| format | article |
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| identifier | ISSN: 0036-1429 |
| ispartof | SIAM journal on numerical analysis, 1984-10, Vol.21 (5), p.985-994 |
| issn | 0036-1429 1095-7170 |
| language | eng |
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| source | ABI/INFORM Global; LOCUS - SIAM's Online Journal Archive; Access via JSTOR |
| subjects | Entropy |
| title | Convergence of an Antidiffusion Lagrange-Euler Scheme for Quasilinear Equations |
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