Application of a finite element method for variational inequalities

AKINLAR M. A.

Journal of Inequalities and Applications, vol.2013, 2013 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-45
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Augmented Lagrangian multipliers method, Finite element method, Optimization, Variational inequalities
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In this paper we explore the application of a finite element method (FEM) to the inequality and Laplacian constrained variational optimization problems. First, we illustrate the connection between the optimization problem and elliptic variational inequalities; secondly, we prove the existence of the solution via the augmented Lagrangian multipliers method. A triangular type FEM is employed in the numerical calculations. Computational results indicate that the present finite element method is a highly efficient technique in these sorts of variational problems involving inequalities. © 2013 Akinlar.