一般区域上三角形线元梯度的超收敛性(英文) |
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引用本文: | 陈传淼
,刘建国.一般区域上三角形线元梯度的超收敛性(英文)[J].湘潭大学自然科学学报,1987(1). |
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作者姓名: | 陈传淼 刘建国 |
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基金项目: | Projects supported by the Science Fund of the Chinese Academy of Sciences |
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摘 要: | Consider second order linear elliptic problem and linear elementProject u~h.Triangulation in each subdomain Ω_j is strongly regular. Atmiddle point z of common side of any two adjacent elements K_1 andK_2 in Ω_j, we define the averaging gradient Du~h(z)=(Du~h(K_1)+Du~h(K_2))/2. With these values we can construct a piecewise linear,continuous function G(u~h) in Ω. If triangulation satisfies 6PC condi-tion or PC condition without interior meeting point, then ||Du-G(u~h)||_(o,∞,Ω)≤ch~2|lnh| ||u||_(3,∞,Ω). If triangulation satisfies PC conditionand A_1,A_2, …, A_N are interior meeting points, Ω_γ={x|x∈Ω,|x-A_j|≥γ>0,j= 1,2,…,N}, then ||Du-G(u~h)||_(0,∞,Ω_γ)≤c_γh~2|lnh| ||u||_(3,∞,Ω.)
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