scholarly journals A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates

2013 ◽  
Vol 254 ◽  
pp. 31-42 ◽  
Author(s):  
Susanne C. Brenner ◽  
Li-yeng Sung ◽  
Hongchao Zhang ◽  
Yi Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Obstacle Problem ◽  
Kirchhoff Plates ◽  
Element Method

An Optimal Adaptive Finite Element Method for an Obstacle Problem

2015 ◽  
Vol 15 (3) ◽  
pp. 259-277 ◽  
Author(s):  
Carsten Carstensen ◽  
Jun Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Obstacle Problem ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Error Estimator ◽  
A Posteriori ◽  
Optimal Complexity ◽  
A Posteriori Error ◽  
Element Method

AbstractThis paper provides a refined a posteriori error control for the obstacle problem with an affine obstacle which allows for a proof of optimal complexity of an adaptive algorithm. This is the first adaptive mesh-refining finite element method known to be of optimal complexity for some variational inequality. The result holds for first-order conforming finite element methods in any spacial dimension based on shape-regular triangulation into simplices for an affine obstacle. The key contribution is the discrete reliability of the a posteriori error estimator from [Numer. Math. 107 (2007), 455–471] in an edge-oriented modification which circumvents the difficulties caused by the non-existence of a positive second-order approximation [Math. Comp. 71 (2002), 1405–1419].

scholarly journals Bubbles Enriched Quadratic Finite Element Method for the 3D-Elliptic Obstacle Problem

2018 ◽  
Vol 18 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Sharat Gaddam ◽  
Thirupathi Gudi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Obstacle Problem ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Three Dimensional ◽  
A Priori Error Estimates ◽  
Priori Error Estimates ◽  
Element Method

AbstractAn optimally convergent (with respect to the regularity) quadratic finite element method for the two-dimensional obstacle problem on simplicial meshes is studied in [14]. There was no analogue of a quadratic finite element method on tetrahedron meshes for the three-dimensional obstacle problem. In this article, a quadratic finite element enriched with element-wise bubble functions is proposed for the three-dimensional elliptic obstacle problem. A priori error estimates are derived to show the optimal convergence of the method with respect to the regularity. Further, a posteriori error estimates are derived to design an adaptive mesh refinement algorithm. A numerical experiment illustrating the theoretical result on a priori error estimates is presented.

scholarly journals Galerkin least squares finite element method for the obstacle problem

2017 ◽  
Vol 313 ◽  
pp. 362-374 ◽  
Author(s):  
Erik Burman ◽  
Peter Hansbo ◽  
Mats G. Larson ◽  
Rolf Stenberg
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Obstacle Problem ◽  
Element Method
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