An estimate for the three-dimensional discrete Green's function and applications

DOI10.1016/j.jmaa.2010.05.002zbMath1194.35013OpenAlexW2029723673MaRDI QIDQ984788

Jinghong Liu, Qiding Zhu, Bo Jia

Publication date: 20 July 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.05.002

zbMATH Keywords

weak estimatesdiscrete Green's functionblock finite elementregularized Green's function

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (7)

Superconvergence of the function value for pentahedral finite elements for an elliptic equation with varying coefficients ⋮ \(L^\infty\)- and \(L^2\)-norms superconvergence of the tetrahedral quadratic finite element ⋮ Green's function for discrete second-order problems with nonlocal boundary conditions ⋮ Local pointwise convergence of the 3D finite element ⋮ Pointwise supercloseness of the displacement for tensor-product quadratic pentahedral finite elements ⋮ Superconvergence of tetrahedral quadratic finite elements for a variable coefficient elliptic equation ⋮ Locally pointwise superconvergence of the tensor-product finite element in three dimensions.

Cites Work

• Natural Superconvergence Points in Three-Dimensional Finite Elements
• Pointwise superconvergence of the gradient for the linear tetrahedral element
• Gradient superconvergence on uniform simplicial partitions of polytopes
• Superconvergence in Finite Element Methods and Meshes That are Locally Symmetric with Respect to a Point
• Pointwise supercloseness of tensor‐product block finite elements
• Maximum‐norm superapproximation of the gradient for the trilinear block finite element
• Equivalent Norms for Sobolev Spaces
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