For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Gr...For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Green's function are introduced.Secondly,some relationship of norms such as L^(2)-norms,W^(1,∞)-norms,and negative-norms in locally smooth subsets of the domainΩis derived.Finally,local pointwise convergence properties of the finite element approximation are obtained.展开更多
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文摘For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Green's function are introduced.Secondly,some relationship of norms such as L^(2)-norms,W^(1,∞)-norms,and negative-norms in locally smooth subsets of the domainΩis derived.Finally,local pointwise convergence properties of the finite element approximation are obtained.
