| 奇型抛物问题的有限元误差估计 |
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| 引用本文： | 王胜兵. 奇型抛物问题的有限元误差估计[J]. 海军工程大学学报, 1991, 0(4) |
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| 作者姓名： | 王胜兵 |
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| 作者单位： | 海军工程学院训练部 |
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| 摘 要： | 本文引入带权的 Sobolev 空间,讨论了奇型线性问题:(?)((?)u)/((?)t)-1/x~(?)(x~aa(x)u′)′=f(t,x) (x,t)∈1×J(?)/((?)x)u(t,0)=u(t,1)=0 t∈Ju(0,x)=φ(x) x∈I式中 I=(0,1),J=[0,T],0<α<3的有限元方法,并在适当条件下,给出了最佳估计:‖u_(?)-u‖_(0,2,a)≤ch~2{‖φ‖_(2,2,a)+[integral 0 to t (‖u‖~2_(2,2,a)+‖u_(?)‖~2_(2,2,a)dt]~(1/2)}‖u_(?)-u‖_(1,2,a)≤ch~2{‖φ‖_(2,2,a)+[integral 0 to t (‖u‖~2_(2,2,a)+‖u_(?)‖~2_(2,2,a)dt]~(1/2)}
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| 关 键 词： | 带权的 Sobolev 空间 奇型抛物问题 有限元 |
Error Estimates of Finite Element for Singular Parabolic Problem |
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| Wang Shengbing. Error Estimates of Finite Element for Singular Parabolic Problem[J]. Journal of Naval University of Engineering, 1991, 0(4) |
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| Authors: | Wang Shengbing |
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| Affiliation: | Wang Shengbing |
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| Abstract: | By introducing weighted Sobolev space,the linear parabolic equation with singular coefficients is studied.The optimal order semidiscrete error estimates for linear finite element is proved: (?) |
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| Keywords: | Weighted Sobolev space Singular parabolic problem Finite element |
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