High-order compact scheme finite difference discretization for Signorini's problem

Abstract

This paper brings out an analysis of the projection iterative algorithm for the numerical solution of the Signorini problem. The very closed connections with the switching method are highlighted. In addition, the relevance of higher-order discretization for Signorini problem is discussed. Thus, a specific iterative solver is developed to address the present fourth and sixth-order compact scheme discretizations. This method is based on a lower-order preconditioning method. Several numerical experiments have been performed to bring light to the accuracy of such method, despite the lack of smoothness at the Signorini boundary.

Keywords:

• Signorini problems
• high-order compact finite difference
• projection iterative method
• low-order preconditioning
• non-linear boundary value

2010 Mathematics Subject Classification:

• 35J65

Acknowledgements

The project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 823731 - CONMECH. This work was also realized with the support of HPC@LR, a Center of competence in High-Performance Computing from the Languedoc-Roussillon region.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

S. Abide http://orcid.org/0000-0002-5448-3525

Additional information

Funding

The project has received funding from the European Commission Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 823731 - CONMECH. This work was also realized with the support of HPC@LR, a Center of competence in High-Performance Computing from the Languedoc-Roussillon region.