Presentation of the Finite Volume Method

Alexandre Ern (1) , Serge Piperno (1) , Dominique Thiéry (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)

Chapter contains sections titled: -1D conservation equations -Classical, weak and entropic solutions -Numerical solution of a conservation law -Numerical solution of hyperbolic systems -High-order, finite volume methods -Application of the finite volume method to the flow development of groundwater -Bibliography

Keywords: finite volume method; Burgers equation; traffic model; Godunov and Riemann problem; hyperbolic

Domains: Analysis of PDEs [math.AP]; Mechanics [physics.med-ph]

Alexandre Ern, Serge Piperno, Dominique Thiéry. Presentation of the Finite Volume Method. Jean-Michel Tanguy. Numerical Methods, John Wiley & Sons, Inc., pp.161-211, 2013, ⟨10.1002/9781118557877.ch8⟩. ⟨hal-03703074⟩