@misc{Arakelyan_Avetik_A,
 author={Arakelyan, Avetik},
 howpublished={online},
 publisher={National Academy of Sciences of Armenia},
 abstract={In this paper we treat the numerical approximation of the two-phase parabolic obstacle-like problem: \[\Delta u -u_t=\lambda^+\cdot\chi_\{\\{u > 0\\}\}-\lambda^-\cdot\chi_\{\\{u < 0\\}\},\quad (t,x)\in (0,T)\times\Omega,\] where \$T < \infty, \lambda^+ ,\lambda^- > 0\$ are Lipschitz continuous functions, and \$\Omega\subset\mathbb\{R\}^n\$ is a bounded domain. We introduce a certain variation form, which allows us to define a notion of viscosity solution. We use defined viscosity solutions framework to apply Barles-Souganidis theory. The numerical projected Gauss-Seidel method is constructed. Although the paper is devoted to the parabolic version of the two-phase obstacle-like problem, we prove convergence of the discretized scheme to the unique viscosity solution for both two-phase parabolic obstacle-like and standard two-phase membrane problem. Numerical simulations are also presented.},
 title={A Finite Difference Method for Two-Phase Parabolic Obstacle-like Problem},
 type={Հոդված},
 keywords={Partial differential equations, Numerical analysis},
}