Abstract
In this paper, we focus on the numerical approximation of the Cahn-Hilliard-Hele-Shaw system. Firstly, based on the idea of the stabilized method, an unconditionally stable linear scheme with second-order accuracy in time and space is proposed, which is modified from the Crank-Nicolson scheme. Secondly, we derive that the proposed numerical scheme is unconditionally stable, without any restriction for the time step size. After a careful calculation, we get discrete error estimates of the time step size τ and space step size h. Finally, numerical simulations of energy dissipation and spinodal decomposition are presented to demonstrate the stability, accuracy and efficiency of the proposed scheme.
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