A hybrid finite element-finite volume method for conservation laws
| hal.structure.identifier | Universität Zürich [Zürich] = University of Zurich [UZH] | |
| dc.contributor.author | ABGRALL, Rémi | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BARSUKOW, Wasilij | |
| dc.date.accessioned | 2024-04-04T02:40:24Z | |
| dc.date.available | 2024-04-04T02:40:24Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191063 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.subject.en | Active Flux | |
| dc.subject.en | high order methods | |
| dc.subject.en | conservation laws Mathematics Subject Classification (2010): 65M06 | |
| dc.subject.en | 65M08 | |
| dc.subject.en | 65M60 | |
| dc.subject.en | 76N99 | |
| dc.title.en | A hybrid finite element-finite volume method for conservation laws | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 2208.14477 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03787579 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03787579v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ABGRALL,%20R%C3%A9mi&BARSUKOW,%20Wasilij&rft.genre=preprint |
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