A decoupled finite difference scheme for the phase separation equation coupled with viscoelasticity in two-space dimension

Abstract In this article, we study the phase separation equation coupled with viscoelasticity in two-space dimension. Pawłow and Zaja̧czkowski proposed the system and gave some mathematical analysis such as the existence of a solution in the series of results. Our purpose is to propose a decoupled finite difference scheme for the model and to show the unique existence of the solution for the scheme and the error estimate. Moreover, several numerical simulations are demonstrated.