Analysis and Estimation of Error Constants for {large{oldmath$P_0$}} and {large{oldmath$P_1$}} Interpolations over Triangular Finite Elements

Journal of Mathematical Sciences

Liu, Xuefeng¹  Kikuchi, Fumio¹ 

关键词: FEM;    error estimates;    triangular finite elements;    interpolation error constants.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Wegivesomefundamentalresultsontheerrorconstantsforthepiecewiseconstantinterpolationfunctionandthepiecewiselinearoneovertriangles.Forthepiecewiselinearone,wemainlyanalyzetheconformingcase,butthepresentresultsalsoappeartobeavailableforthenon-conformingcase.Weobtainexplicitrelationsfortheupperboundsoftheconstants,andanalyzedependenceofsuchconstantsonthegeometricparametersoftriangles.Inparticular,weexplicitlydeterminesomespecialconstantsincludingtheBabuvska-Azizconstant,whichplaysanessentialroleintheinterpolationerrorestimationofthelineartriangularfiniteelement.Theobtainedresultsareexpectedtobewidelyusedforaprioriandaposteriorierrorestimationsinadaptivecomputationandnumericalverificationofnumericalsolutionsbasedonthetriangularfiniteelements.Wealsogivesomenumericalresultsfortheerrorconstantsandforaposterioriestimatesofsomeeigenvaluesrelatedtotheerrorconstants.

【 授权许可】

Unknown