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Finite element methods for Hamiltonian PDEs

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GCS - Geometry, compatibility and structure preservation in computational differential equations

Hamiltonian ODEs satisfy a symplectic conservation law, and there are many advantages to using numerical integrators that preserves this structure. This talk will discuss how the canonical Hamiltonian structure, and its preservation by a numerical method, can be generalized to PDEs. I will also provide a basic introduction to the finite element method and, time permitting, discuss how some classic symplectic integrators can be understood from this point of view.




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