Violaine Louvet

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In this paper we mathematically characterize through a Lie formalism the local errors induced by operator splitting when solving nonlinear reaction-diffusion equations, especially in the non-asymptotic regime. The non-asymptotic regime is often attained in practice when the splitting time step is much larger than some of the scales associated with either(More)
We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reaction fronts,(More)
Reaction-diffusion systems involving a large number of unknowns and a wide spectrum of scales in space and time model various phenomena across disciplines such as combustion dynamics , atmospheric science, or biomedical engineering. The numerical solution of these multi-scale systems of partial differential equations entails specific challenges due to the(More)
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