On Time-Discretization of the 2d Euler Equation by a Symplectic Crouch-Grossman Integrator - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

On Time-Discretization of the 2d Euler Equation by a Symplectic Crouch-Grossman Integrator

Romain Horsin
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Résumé

We consider time discretizations of the two-dimensional Euler equation written in vorticity form. The discretization method uses a Crouch-Grossman integrator that proceeds in two stages: first freezing the velocity vector field at the beginning of the time step, and then solve the resulting elementary transport equation by using a symplectic integrator to discretize in time the flow of the associated Hamiltonian differential equation. We prove that these schemes yield order one approximations of the exact solutions, and provide error estimates in Sobolev norms.
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Dates et versions

hal-01910613 , version 1 (01-11-2018)

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Romain Horsin. On Time-Discretization of the 2d Euler Equation by a Symplectic Crouch-Grossman Integrator. 2018. ⟨hal-01910613⟩
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