An iterative algorithm for elliptic variational inequalities of the second kind

Abstract

In this paper, we propose an iterative algorithm for a simplified friction problem which is formulated as an elliptic variational inequality of the second kind. We approximate the simplified friction problem by a discrete system with the finite element method. Based on the use of the linearized technique and by constructing a particular function, we put forward the new algorithm to get the discrete solution. This algorithm is attractive due to its simple proof of convergence and easy implementation. A linear equation is solved in each iteration. Numerical results confirm that our algorithm is efficient and mesh independent.

Keywords:

• linearization
• convergence
• elliptic variational inequality of the second kind
• algorithm
• finite element method

2010 AMS Subject Classifications:

• 65L60
• 90C33

Acknowledgements

This work is supported by Key Project of NSFC (Grant No. 91130004) and ZPNSFC (Grant No. LY12A01023).