Efficient and reliable hierarchical error estimates for an elliptic obstacle problem

2011 ◽  
Vol 61 (3) ◽  
pp. 344-355 ◽  
Author(s):  
Qingsong Zou
Keyword(s):  
Error Estimates ◽  
Obstacle Problem

SHARP ERROR ANALYSIS FOR CURVATURE DEPENDENT EVOLVING FRONTS

1993 ◽  
Vol 03 (06) ◽  
pp. 711-723 ◽  
Author(s):  
RICARDO H. NOCHETTO ◽  
MAURIZIO PAOLINI ◽  
CLAUDIO VERDI
Keyword(s):  
Error Analysis ◽  
Small Parameter ◽  
Error Estimates ◽  
Distance Function ◽  
Mean Curvature ◽  
Obstacle Problem ◽  
Singularly Perturbed ◽  
Forcing Term ◽  
Formal Asymptotics ◽  
Sharp Error

The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter ε>0. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order [Formula: see text] are derived for smooth evolutions, that is before singularities develop. Key ingredients are the construction of sub(super)-solutions containing several shape corrections dictated by formal asymptotics, and the use of a modified distance function.

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 Finite element estimates for a class of nonlinear variational inequalities

1993 ◽  
Vol 16 (3) ◽  
pp. 503-509 ◽  
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Applied Sciences ◽  
Finite Element ◽  
Approximate Solution ◽  
Variational Inequalities ◽  
Error Estimates ◽  
Obstacle Problem ◽  
Nonlinear Problems ◽  
Highly Nonlinear ◽  
Unilateral Problems ◽  
Special Case

It is well known that a wide class of obstacle and unilateral problems arising in pure and applied sciences can be studied in a general and unifield framework of variational inequalities. In this paper, we derive the error estimates for the finite element approximate solution for a class of highly nonlinear variational inequalities encountered in the field of elasticity and glaciology in terms ofW1,p(Ω)andLp(Ω)-norms. As a special case, we obtain the well-known error estimates for the corresponding linear obstacle problem and nonlinear problems.

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