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

LI Can-hua; CHEN Chuan-miao

doi:10.3879/j.issn.1000-0887.2011.07.011

Volume 32 Issue 7

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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

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

doi: 10.3879/j.issn.1000-0887.2011.07.011

College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China

Received Date: 2010-10-18
Rev Recd Date: 2011-03-25
Publish Date: 2011-07-15

Abstract

Abstract

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.
- averaging discontinuous finite element,
- ultraconvergence,
- Hamiltonian system,
- momentum conservation

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References(16)

References

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