Consider a second-order elliptic boundary value problem in three dimensions with locally smooth coefficients and solution. Discuss local superconvergence estimates for the tensor-product finite element approximation on a regular family of rectangular meshes. It will be shown that, by the estimates for the discrete Green’s function and discrete derivative Green’s function, and the relationship of norms in the finite element space such as L² -norms, W^1,∞ -norms, and negative-norms in locally smooth subsets of the domain Ω, locally pointwise superconvergence occurs in function values and derivatives.

中文翻译：

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张量积有限元在三维上的局部逐点超收敛

考虑具有局部平滑系数和解的三维二阶椭圆边值问题。讨论矩形网格的规则族上张量积有限元逼近的局部超收敛估计。将示出的是，通过该估计的离散格林函数和离散导格林函数，和规范在有限元空间，如关系大号² -norms，w ^ ^1，∞ -norms，和负规范本地函数值和导数中出现了域Ω的平滑子集，局部逐点超收敛。