Superconvergence of tetrahedral quadratic finite elements for a variable coefficient elliptic equation

2012 ◽  
Vol 29 (3) ◽  
pp. 1043-1055 ◽  
Author(s):  
Jinghong Liu ◽  
Gui Hu ◽  
Qiding Zhu
Keyword(s):  
Finite Elements ◽  
Elliptic Equation ◽  
Variable Coefficient ◽  
Quadratic Finite Elements

scholarly journals On Superconvergence of a Gradient for Finite Element Methods for an Elliptic Equation with the Nonsmooth Right–hand Side

2002 ◽  
Vol 2 (3) ◽  
pp. 295-321 ◽  
Author(s):  
Alexander Zlotnik
Keyword(s):  
Finite Elements ◽  
Elliptic Equation ◽  
Error Estimates ◽  
Dirichlet Boundary ◽  
A Priori ◽  
Boundary Function ◽  
Right Hand ◽  
Priori Error Estimates ◽  
The Right ◽  
2D And 3D

AbstractThe elliptic equation under the nonhomogeneous Dirichlet boundary condition in 2D and 3D cases is solved. A rectangular nonuniform partition of a domain and polylinear finite elements are taken. For the interpolant of the exact solution u, a priori error estimates are proved provided that u possesses a weakened smoothness. Next error estimates are in terms of data. An estimate is established for the right–hand side f of the equation having a generalized smoothness. Error estimates are derived in the case of f which is not compatible with the boundary function. The proofs are based on some propositions from the theory of functions. The corresponding lower error estimates are also included; they justify the sharpness of the estimates without the logarithmic multipliers. Finally, we prove similar results in the case of 2D linear finite elements and a uniform partition.

scholarly journals Curved affine quadratic finite elements

1995 ◽  
Vol 63 (1-3) ◽  
pp. 333-339 ◽  
Author(s):  
Stanislav Koukal ◽  
Michal Křížek
Keyword(s):  
Finite Elements ◽  
Quadratic Finite Elements

scholarly journals Bivariate C 1 Quadratic Finite Elements and Vertex Splines

1990 ◽  
Vol 54 (189) ◽  
pp. 169
Author(s):  
Charles K. Chui ◽  
Tian-Xiao He
Keyword(s):  
Finite Elements ◽  
Quadratic Finite Elements

Bivariate $C\sp 1$ quadratic finite elements and vertex splines

1990 ◽  
Vol 54 (189) ◽  
pp. 169-169
Author(s):  
Charles K. Chui ◽  
Tian Xiao He
Keyword(s):  
Finite Elements ◽  
Quadratic Finite Elements

scholarly journals Superconvergence of the function value for pentahedral finite elements for an elliptic equation with varying coefficients

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jinghong Liu ◽  
Qiding Zhu
Keyword(s):  
Finite Element ◽  
Green Function ◽  
Finite Elements ◽  
Elliptic Equation ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
True Solution ◽  
Varying Coefficients ◽  
Fundamental Estimate

AbstractIn this article, for an elliptic equation with varying coefficients, we first derive an interpolation fundamental estimate for the $\mathcal{P}_{2}(x,y)\otimes \mathcal{P}_{2}(z)$P2(x,y)⊗P2(z) pentahedral finite element over uniform partitions of the domain. Then combined with the estimate for the $W^{2,1}$W2,1-seminorm of the discrete Green function, superconvergence of the function value between the finite element approximation and the corresponding interpolant to the true solution is given.

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