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IMA Journal of Numerical Analysis Advance Access originally published online on November 10, 2006
IMA Journal of Numerical Analysis 2007 27(3):616-630; doi:10.1093/imanum/drl033
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Analysis of ADER and ADER-WAF schemes

V. A. Titarev{dagger} and E. F. Toro

Department of Civil and Environmental Engineering, Laboratory of Applied Mathematics, Faculty of Engineering, University of Trento, Via Mesiano, 77, 38050 Trento, Italy

{dagger} Email: titarev{at}ing.unitn.it, titarev{at}mail.ru

Received on 3 October 2005. Revised on 5 October 2006.


  Abstract

We study stability properties and truncation errors of the finite-volume ADER schemes on structured meshes as applied to the linear advection equation with constant coefficients in one-, two- and three-spatial dimensions. Stability of linear ADER schemes is analysed by means of the von Neumann method. For nonlinear schemes, we deduce the stability region from numerical experiments. The truncation error analysis is carried out for linear ADER schemes in one-, two- and three-space dimensions and for nonlinear ADER schemes in one-space dimension.

Key Words: ADER; derivative Riemann problem; high-order schemes; weighted essentially nonoscillatory; multiple space dimensions


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