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Exact Solutions and Conservation Laws of the Joseph-Egri Equation with Power Law Nonlinearity Read chapter Read first chapter

2015 | OriginalPaper | Chapter

SIAC Filtering for Nonlinear Hyperbolic Equations

Authors : Xiaozhou Li, Jennifer K. Ryan

Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Publisher: Springer International Publishing

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Abstract

We present the results of the symmetric and one-sided smoothness-increasing accuracy-conserving (SIAC) filter applied to a discontinuous Galerkin (DG) approximation for two examples of nonlinear hyperbolic conservation laws. The traditional symmetric SIAC filter relies on having a translation invariant mesh, periodic boundary conditions, and linear equations. However, for practical applications that are modeled by nonlinear hyperbolic equations, this is not feasible. Instead we must concentrate on a filter that allows error reduction for nonuniform/unstructured meshes and nonperiodic boundary conditions for nonlinear hyperbolic equations. This proceedings is an introductory exploration into the feasibility of these requirements for efficient filtering of nonlinear equations.

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previous chapter Controllability of Second Order Impulsive Differential Systems in Banach Spaces
next chapter Structural Analysis and Dummy Derivatives: Some Relations
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Metadata
Title
SIAC Filtering for Nonlinear Hyperbolic Equations
Authors
Xiaozhou Li
Jennifer K. Ryan
Copyright Year
2015
Book
Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Print ISBN: 978-3-319-12306-6

Electronic ISBN: 978-3-319-12307-3

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12307-3_41

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