Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method

  • Avetik Arakelyan Institute of Mathematics NAS of Armenia, Baghramyan 24/5, 0019 Yerevan, Armenia
  • Rafayel Barkhudaryan Institute of Mathematics NAS of Armenia, Baghramyan 24/5, 0019 Yerevan, Armenia http://orcid.org/0000-0002-9794-9284
  • Michael Poghosyan Department of Mathematics and Mechanics, Yerevan State University, Alex Manoogian 1, 0025, Yerevan, Armenia

Abstract

We propose an algorithm to solve the two-phase obstacle problem by finite difference method. We prove the existence and uniqueness of the solution of the discrete nonlinear system and obtain an error estimate for the corresponding regularization. Also we prove the convergence of the proposed numerical algorithm. At the end of the paper we present some numerical simulations.

Published
2015-12-10
How to Cite
Arakelyan, A., Barkhudaryan, R., & Poghosyan, M. (2015). Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method. Armenian Journal of Mathematics, 7(2), 164-182. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/118