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Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem. (English) Zbl 1300.65063
The author is concerned with higher-order maximum principle preserving schemes for hyperbolic conservation laws within the flux limiters. The approach relies on decoupling a sequence of parameters embedded in a group of explicit inequalities which preserves both the global maximum principles and the accuracy of the underlying scheme. Several numerical tests are performed which support the theoretical findings.

MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35B50 Maximum principles in context of PDEs
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