Hamilton Non Coordination Algorithm And Conservation Of The System

Feng[2][3]proposed symplectic algorithms and the theories forHamiltonian systems, constructed piles of symplectic schemes as well.Non-conforming finite element method relaxes the continuity of thecell boundary. En[4]~[7]proposed variational principle for unconventionalHamiltonian system, this variational principle not only characterizesinitial-value problem of this dynamic, but also has a natural symplecticstructure.The nonconforming finite element method bases on unconventionalvariational principle, it’s feasible for complex boundary conditions, andreflect the whole characteristics of the dynamic, which make symplecticalgorithms a wide range of applications vitality.Part I mainly talks about Hamiltonian mechanics and the basicknowledge of symplectic algorithm; part II briefly introducesunconventional variational principle for Hamiltonian system; part III talksabout FEM and nonconforming FEM; part IV constructs some kind ofnonconforming symplectic FEM to solve Hamiltonian system; part V issynthesis report which is refined after large amount of reading,according to the graduation requirements of Department ofMathematics, Shanghai JiaoTong University.Innovative works: 1. Propose some special non-conforming symplectic finite elementmethod, it’s energy conversation;2. Create some special non-conforming finite element method andprove they are symplectic for linear Hamiltonian system;3. Prove and design non-conforming finite element method fornonlinear Hamiltonian system;4. Related numerical examples, prove the validity of this algorithm.