A priori error estimates for the finite element approximation of an obstacle problem

2000 ◽  
Vol 7 (1) ◽  
pp. 175-181 ◽  
Author(s):  
Cheon Seoung Ryoo
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Obstacle Problem ◽  
A Priori ◽  
Finite Element Approximation ◽  
A Priori Error Estimates ◽  
Element Approximation ◽  
Priori Error Estimates

A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

2014 ◽  
Vol 6 (5) ◽  
pp. 552-569 ◽  
Author(s):  
Wanfang Shen ◽  
Liang Ge ◽  
Danping Yang ◽  
Wenbin Liu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
A Priori ◽  
Mathematical Formulation ◽  
Finite Element Approximation ◽  
A Priori Error Estimates ◽  
Element Approximation ◽  
Weak Formulation ◽  
Priori Error Estimates

AbstractIn this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in H1 and L2 norms. Furthermore some numerical tests are presented to verify the theoretical results.

scholarly journals A priori error estimates for the space-time finite element approximation of a quasilinear gradient enhanced damage model

2021 ◽  
Author(s):  
Marita Holtmannspötter
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
A Priori ◽  
Damage Model ◽  
Space Time ◽  
A Priori Error Estimates ◽  
Element Approximation ◽  
Element Discretization ◽  
Priori Error Estimates ◽  
Almost All

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a quasilinear gradient enhanced damage model. The model equations are of a special structure as the state equation consists of two quasilinear elliptic PDEs which have to be fulfilled at almost all times coupled with a nonsmooth, semilinear ODE that has to hold true in almost all points in space. The system is discretized by a constant discontinuous Galerkin method in time and usual conforming linear finite elements in space. Numerical experiments are added to illustrate the proven rates of convergence.

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.

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