LI Can-hua, CHEN Chuan-miao. Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System[J]. Applied Mathematics and Mechanics, 2011, 32(7): 883-894. doi: 10.3879/j.issn.1000-0887.2011.07.011
 Citation: LI Can-hua, CHEN Chuan-miao. Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System[J]. Applied Mathematics and Mechanics, 2011, 32(7): 883-894.

# Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System

##### doi: 10.3879/j.issn.1000-0887.2011.07.011
• Received Date: 2010-10-18
• Rev Recd Date: 2011-03-25
• Publish Date: 2011-07-15
• The k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations was discussed. When k waseven, it was proved that the averaging numerical flux (the average of left and right lmiits for discon tinuous finite element at nodes) had the optmial order ultraconvergence 2k + 2. For non linear Hamiltonian systems (e. g., S chrêdinger equation and Kepler system) with momentum conservation, it was found that the discon tinuous finite element methods preserve momentum at nodes. These properties were confirmed by numerical expermients.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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