An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws

Jan Giesselmann; Fabian Meyer; Christian Rohde

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arXiv · 1908.09612

An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws

Jan Giesselmann·Fabian Meyer·Christian Rohde

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Abstract

We present an a posteriori error analysis for one-dimensional random hyperbolic systems of conservation laws. For the discretization of the random space we consider the Non-Intrusive Spectral Projection method, the spatio-temporal discretization uses the Runge--Kutta Discontinuous Galerkin method. We derive an a posteriori error estimator using smooth reconstructions of the numerical solution, which combined with the relative entropy stability framework yields computable error bounds for the space-stochastic discretization error. Moreover, we show that the estimator admits a splitting into a stochastic and deterministic part.

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BibTeX RIS

Jan Giesselmann, Fabian Meyer, Christian Rohde. 2019-08-26. An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws. https://arxiv.org/abs/1908.09612

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