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Medientyp:
E-Artikel
Titel:
Quasimonotone Schemes for Scalar Conservation Laws. Part I
Beteiligte:
Cockburn, Bernardo
Erschienen:
Society for Industrial and Applied Mathematics, 1989
Erschienen in:
SIAM Journal on Numerical Analysis, 26 (1989) 6, Seite 1325-1341
Sprache:
Englisch
ISSN:
0036-1429
Entstehung:
Anmerkungen:
Beschreibung:
In this work, the quasimonotone schemes for scalar conservation laws are introduced. These new schemes share with monotone schemes both maximum principles and convergence to the entropy solution. However, they are not necessarily first-order accurate. They include both finite-difference schemes (that are total variation diminishing (TVD)) and finite-element ones (that are not TVD), they can be either explicit or implicit; and they can be used with time-dependent grids. They can be defined for d-space variables in the case of a grid that is a Cartesian product of one-dimensional partitions. Error estimates are provided. Part I covers the quasimonotone finite-difference schemes in one dimension. Part II is devoted to quasimonotone finite-element schemes, also in one dimension. Finally, Part III discusses the general case.