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Numerical methods for Hamiltonian PDEs. (English) Zbl 1090.65138
Summary: The paper provides an introduction and survey of conservative discretization methods for Hamiltonian partial differential equations. The emphasis is on variational, symplectic and multi-symplectic methods. The derivation of methods as well as some of their fundamental geometric properties are discussed. Basic principles are illustrated by means of examples from wave and fluid dynamics.
MSC:
65P10Numerical methods for Hamiltonian systems including symplectic integrators
37M15Symplectic integrators (dynamical systems)
37K05Hamiltonian structures, symmetries, variational principles, conservation laws