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Second‐order finite‐volume schemes for a non‐linear hyperbolic equation: error estimate
Author(s) -
ChainaisHillairet Claire
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(20000325)23:5<467::aid-mma124>3.0.co;2-7
Subject(s) - mathematics , finite volume method , hyperbolic partial differential equation , entropy (arrow of time) , order (exchange) , volume (thermodynamics) , error analysis , mathematical analysis , partial differential equation , thermodynamics , physics , finance , economics
We study second‐order finite‐volume schemes for the non‐linear hyperbolic equation u t ( x , t ) + div F ( x , t , u ( x , t )) = 0 with initial condition u 0 . The main result is the error estimate between the approximate solution given by the scheme and the entropy solution. It is based on some stability properties verified by the scheme and on a discrete entropy inequality. If u 0 ∈ L ∞ ∩ BV loc (ℝ N ), we get an error estimate of order h 1/4 , where h defines the size of the mesh. Copyright © 2000 John Wiley & Sons, Ltd.