Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

Error Estimates for Linear Hyperbolic Equations

  • Chi-Wang Shu
Reference work entry
First Online:
DOI: https://doi.org/10.1007/978-3-540-70529-1_546
How to cite

Mathematics Subject Classification

65M15; 65M06; 65M60; 65M70

Synonyms

Discontinuous Galerkin method (DG); Finite difference method (FD); Finite element method (FE); Finite volume method (FV); Ordinary differential equation (ODE); Partial differential equation (PDE); Strong stability preserving (SSP); Total variation diminishing (TVD)

Short Definition

We discuss error estimates for finite difference (FD), finite volume (FV), finite element (FE), and spectral methods for solving linear hyperbolic equations, with smooth or discontinuous solutions.

Description

Hyperbolic equations arise often in computational mechanics and other areas of computational sciences, for example, they can describe various wave propagation phenomena, such as water waves, electromagnetic waves, aeroacoustic waves, and shock waves in gas dynamics. In this entry we are concerned with linear hyperbolic equations, which take the form
$$\displaystyle{ u_{t} + Au_{x} = 0 }$$
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Chi-Wang Shu
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA