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Interplay Between Diffusion Anisotropy and Mesh Skewness in Hybrid High-Order Schemes Read chapter Read first chapter

2020 | OriginalPaper | Chapter

A Hybrid Discontinuous Galerkin Method for Transport Equations on Networks

Authors : Herbert Egger, Nora Philippi

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Publisher: Springer International Publishing

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Abstract

We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a mathematical energy which allows us to prove existence of unique solutions. We then consider the space discretization by a hybrid discontinuous Galerkin method which provides a suitable upwind mechanism to handle the transport problem and allows to incorporate the coupling conditions in a natural manner. In addition, the method inherits mass conservation and stability of the continuous problem. Order optimal convergence rates are established and illustrated by numerical tests.

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previous chapter Space-Time Discontinuous Galerkin Methods for Linear Hyperbolic Systems and the Application to the Forward Problem in Seismic Imaging
next chapter MUSCL Discretization for the Fluid Flow Convection Operator on Staggered Meshes
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Metadata
Title
A Hybrid Discontinuous Galerkin Method for Transport Equations on Networks
Authors
Herbert Egger
Nora Philippi
Copyright Year
2020
Book
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Print ISBN: 978-3-030-43650-6

Electronic ISBN: 978-3-030-43651-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-43651-3_45

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