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Generalised Polynomial Chaos for a Class of Linear Conservation Laws

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Abstract

Mathematical modelling of dynamical systems often yields partial differential equations (PDEs) in time and space, which represent a conservation law possibly including a source term. Uncertainties in physical parameters can be described by random variables. To resolve the stochastic model, the Galerkin technique of the generalised polynomial chaos results in a larger coupled system of PDEs. We consider a certain class of linear systems of conservation laws, which exhibit a hyperbolic structure. Accordingly, we analyse the hyperbolicity of the corresponding coupled system of linear conservation laws from the polynomial chaos. Numerical results of two illustrative examples are presented.

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Authors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik und Numerische Mathematik, Bergische Universität Wuppertal, Gaußstr. 20, 42119, Wuppertal, Germany

    Roland Pulch

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Dongbin Xiu

Authors
  1. Roland Pulch
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  2. Dongbin Xiu
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Correspondence to Roland Pulch.

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Pulch, R., Xiu, D. Generalised Polynomial Chaos for a Class of Linear Conservation Laws. J Sci Comput 51, 293–312 (2012). https://doi.org/10.1007/s10915-011-9511-5

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  • DOI: https://doi.org/10.1007/s10915-011-9511-5

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