Journal of Scientific Computing

, Volume 81, Issue 3, pp 2388–2412

# Virtual Element Method for an Elliptic Hemivariational Inequality with Applications to Contact Mechanics

• Fang Feng
• Weimin Han
• Jianguo Huang
Article

## Abstract

This paper is on the numerical solution of an elliptic hemivariational inequality by the virtual element method. We introduce an abstract framework of the numerical method and provide an error analysis. We then apply the virtual element method to solve two contact problems: a bilateral contact problem with friction and a frictionless normal compliance contact problem. Error estimates of their numerical solutions are derived, which are of optimal order for the linear virtual element method, under appropriate solution regularity assumptions. The discrete problem can be formulated as an optimization problem for a difference of two convex (DC) functions, and a convergent algorithm is introduced to solve it. Numerical examples are reported to show the performance of the proposed methods.

## Keywords

Virtual element method Hemivariational inequality Error estimate Double bundle method

## Notes

### Acknowledgements

The authors would like to thank the referees for their valuable suggestions and comments on an early version of the paper.

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## Authors and Affiliations

• Fang Feng
• 1
• Weimin Han
• 2
• Jianguo Huang
• 1
1. 1.School of Mathematical Sciences, and MOE-LSCShanghai Jiao Tong UniversityShanghaiChina
2. 2.Department of MathematicsUniversity of IowaIowa CityUSA