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Discrete mechanics and the finite element method. (English) Zbl 1068.70500
Summary: We explore applications of the Finite Element Method (FEM) to both Veselov and Lee discrete mechanics in this paper. Based on the FEM, disretizations of continuous Lagrangians are developed and corresponding integrators are obtained. Error estimates for variational integrators are also given.

MSC:
70-08 Computational methods for problems pertaining to mechanics of particles and systems
70G75 Variational methods for problems in mechanics
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
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