Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws
Abstract
We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is quantified at each interface of the mesh, which enables us to prove a weak-$BV$ estimate for the numerical approximation under a strengthened CFL condition. Then we derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical $\mathcal{O}(h^{1/4})$ estimate in $L^2$ under this strengthened CFL condition.
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© 2016, Society for Industrial and Applied Mathematics.
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Submitted: 9 June 2015
Accepted: 4 February 2016
Published online: 21 April 2016
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Centre National de la Recherche Scientifique http://dx.doi.org/10.13039/501100004794
Commissariat à l'Énergie Atomique et aux Énergies Alternatives http://dx.doi.org/10.13039/501100006489
Université Pierre et Marie Curie http://dx.doi.org/10.13039/501100005737
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