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

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

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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 numeri...

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Main Authors: Avetik Arakelyan, Rafayel Barkhudaryan, Michael Poghosyan
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2015-12-01
Series:Armenian Journal of Mathematics
Online Access:http://test.armjmath.sci.am/index.php/ajm/article/view/118
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spelling doaj-622fbdcc68ce41019a6a217e57e913652020-11-24T23:21:44ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632015-12-0172Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference MethodAvetik Arakelyan0Rafayel Barkhudaryan1Michael Poghosyan2Institute of Mathematics NAS of Armenia, Baghramyan 24/5, 0019 Yerevan, ArmeniaInstitute of Mathematics NAS of Armenia, Baghramyan 24/5, 0019 Yerevan, ArmeniaDepartment of Mathematics and Mechanics, Yerevan State University, Alex Manoogian 1, 0025, Yerevan, Armenia 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. http://test.armjmath.sci.am/index.php/ajm/article/view/118
collection DOAJ
language English
format Article
sources DOAJ
author Avetik Arakelyan
Rafayel Barkhudaryan
Michael Poghosyan
spellingShingle Avetik Arakelyan
Rafayel Barkhudaryan
Michael Poghosyan
Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method
Armenian Journal of Mathematics
author_facet Avetik Arakelyan
Rafayel Barkhudaryan
Michael Poghosyan
author_sort Avetik Arakelyan
title Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method
title_short Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method
title_full Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method
title_fullStr Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method
title_full_unstemmed Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method
title_sort numerical solution of the two-phase obstacle problem by finite difference method
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2015-12-01
description 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.
url http://test.armjmath.sci.am/index.php/ajm/article/view/118
work_keys_str_mv AT avetikarakelyan numericalsolutionofthetwophaseobstacleproblembyfinitedifferencemethod
AT rafayelbarkhudaryan numericalsolutionofthetwophaseobstacleproblembyfinitedifferencemethod
AT michaelpoghosyan numericalsolutionofthetwophaseobstacleproblembyfinitedifferencemethod
_version_ 1725570223470280704

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