ABGRALL, Rémi; BARSUKOW, Wasilij

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ABGRALL, Rémi
Universität Zürich [Zürich] = University of Zurich [UZH]

BARSUKOW, Wasilij
Institut de Mathématiques de Bordeaux [IMB]

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We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside the cell. To lowest (3rd) order this method reduces to the Active Flux method. The update of the moments is achieved immediately by integrating the conservation law over the cell, integrating by parts and employing the continuity across cell interfaces. We propose two ways how the point values can be updated in time: either by first deriving a semi-discrete method that uses a finite-difference-type formula to approximate the spatial derivative, and integrating this method e.g. with a Runge-Kutta scheme, or by using a characteristics-based update, which is inspired by the original (fully discrete) Active Flux method. We analyze stability and accuracy of the resulting methods.< Leer menos

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Active Flux

high order methods

conservation laws Mathematics Subject Classification (2010): 65M06

65M08

65M60

76N99

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A hybrid finite element-finite volume method for conservation laws

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