Localization effects and measure source terms in numerical schemes for balance laws

Abstract. This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Laurent Gosse
• Keywords: MOC 2002, Nonhomogeneous Scalar Laws, Nonlinear Conservation Laws, Numerical Schemes