A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems

2005 ◽  
Vol 54 (3-4) ◽  
pp. 555-576 ◽  
Author(s):  
S. Hüeber ◽  
M. Mair ◽  
B.I. Wohlmuth
Keyword(s):  
Finite Elements ◽  
Error Estimates ◽  
A Priori ◽  
Contact Problems ◽  
Active Set ◽  
Active Set Strategy ◽  
Primal Dual ◽  
Priori Error Estimates ◽  
Quadratic Finite Elements ◽  
Multibody Contact

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.

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