Numerical Solution of the Two-PhaseObstacle Problem by Finite DifferenceMethod

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Numerical Solution of the Two-PhaseObstacle Problem by Finite DifferenceMethod Avetik Arakelyan

We propose an algorithm to solve thetwo-phaseobstacle problemby finite difference method. We prove the ex-istence and uniqueness of the solution of the discrete nonlinearsystem and obtain an error estimate for the corresponding reg-ularization. Also we prove the convergence of the proposed nu-merical algorithm. At the end of the paper we present somenumerical simulations.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/118 Armenian Journal of Mathematics, 7(2) 164-182

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Keywords

Free Boundary Problem, Two-Phase Membrane Problem, Two-Phase Obstacle Problem, Finite Difference Method

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