Multiresolution analysis for stochastic hyperbolic conservation laws

IMA Journal of Numerical Analysis, vol. 44, pp. 536–575

Abstract

Abstract A multiresolution analysis (MRA) for solving stochastic conservation laws is proposed. Using a novel adaptation strategy and a higher-dimensional deterministic problem, a discontinuous Galerkin (DG) solver is derived. An MRA of the DG spaces for the proposed adaptation strategy is presented. Numerical results show that in the case of general stochastic distributions the performance of the DG solver is significantly improved by the novel adaptive strategy. The gain in efficiency is validated in computational experiments.

Authors 3

1. Michaël Herty Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany

2. Adrian Kolb corresponding Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany

3. Siegfried Müller Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany