an:01198501
Zbl 0955.65069
Bouchut, F.; Perthame, B.
Kruzkov's estimates for scalar conservation laws revisited
EN
Trans. Am. Math. Soc. 350, No. 7, 2847-2870 (1998).
00051007
1998
j
65M15 65M06 65M12 35L65
multidimensional scalar conservation laws; error estimates; entropy inequalities; convergence; finite volume methods
Summary: We give a synthetic statement of Kruzhkov-type estimates for multidimensional scalar conservation laws [cf. \textit{S. N. Kruzhkov}, Mat. Sb., N. Ser. 81(123), 228-255 (1970; Zbl 0202.11203)]. We apply it to obtain various estimates for different approximation problems. In particular, we recover for a model equation the rate of convergence in \(h^{1/4}\) known for finite volume methods on unstructured grids.
Zbl 0215.16203; Zbl 0202.11203