The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem

2002 ◽  
Vol 40 (1) ◽  
pp. 307-318 ◽  
Author(s):  
Zhiqiang Cai ◽  
Byeong Chun Shin
Keyword(s):  
Boundary Value Problem ◽  
Least Squares ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Order System ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
First Order

Superconvergence Recovery for the Gradient of the Trilinear Finite Element

2011 ◽  
Vol 268-270 ◽  
pp. 1021-1024
Author(s):  
Jing Hong Liu ◽  
De Cheng Yin
Keyword(s):  
Finite Element ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Three Dimensions ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Interpolation Postprocessing ◽  
Linear Elements

For a second-order elliptic boundary value problem in three dimensions, we use an interpolation postprocessing technique to obtain recovered gradients of tri- linear elements over regular meshes. Further, superconvergence of these gradients are proved.

scholarly journals Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hongsen Fan ◽  
Zhiying Deng
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Exponent ◽  
Positive Solution ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity

AbstractIn this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.

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