Abstract
This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux (the average of left and right limits for the discontinuous finite element at nodes) has the optimal-order ultraconvergence 2k + 2. For nonlinear Hamiltonian systems (e.g., Schrödinger equation and Kepler system) with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.
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Project supported by the National Natural Science Foundation of China (No. 10771063)
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Li, Ch., Chen, Cm. Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system. Appl. Math. Mech.-Engl. Ed. 32, 943–956 (2011). https://doi.org/10.1007/s10483-011-1471-8
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DOI: https://doi.org/10.1007/s10483-011-1471-8