Sobolev型方程各向异性网格下Wilson元的高精度分析  

HIGHER ACCURACY ANALYSIS FOR THE WILSON ELEMENT TO SOBOLEV TYPE EQUATION ON ANISOTROPIC MESHES

作　　者：石东洋[1] 任金城[2] 郝晓斌[1] 

机构地区：[1]郑州大学数学系,郑州450052 [2]商丘师范学院数学系,商丘476000

出　　处：《高等学校计算数学学报》2009年第2期169-180,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10671184);河南省高等学校创新人才培养工程基金(2002-219)

摘　　要：Sobolev方程在流体穿过裂缝岩石的渗透理论，土壤中湿气的转移问题，不同介质的热传导问题等许多物理问题中都有广泛的应用，因此已有许多文献研究此方程[2,6,8,9,11]，但这些研究都是基于对剖分的正则性条件或拟一致假设，In this paper, higher accuracy analysis of the Wilson element to Sobolev equation is discussed under anisotropic meshes. The superclose property, which is as the same as results on regular meshes are derived. Then, the superconvergence is obtained through the interpolation postprocessing technique. Two order higher convergence rate than general error estimate in H^1-norm is derived by use of extrapolation.

关 键 词：SOBOLEV型方程 WILSON元 各向异性网格 精度分析 SOBOLEV方程 热传导问题 正则性条件 渗透理论 

分 类 号：O241.82[理学—计算数学] O242.21[理学—数学]