## THERMAL SCIENCE

International Scientific Journal

### CONVERGENCE ANALYSIS OF THE ENERGY-STABLE NUMERICAL SCHEMES FOR THE CAHN-HILLIARD EQUATION

**ABSTRACT**

In this paper we present a second order numerical scheme for the Cahn-Hilliard equation, with a Fourier pseudo-spectral approximation in space. An additional Douglas-Dupont regularization term is introduced, which ensures the energy stability. The bound of numerical solution in H2h and l∞ norms are obtained at a theoretical level. Moreover, for the global nature of the pseudo-spectral method, we propose a linear iteration algorithm to solve the non-linear system, due to the implicit treatment for the non-linear term. Some numerical simulations verify the efficiency of iteration algorithm.

**KEYWORDS**

PAPER SUBMITTED: 2021-06-15

PAPER REVISED: 2021-07-12

PAPER ACCEPTED: 2021-07-21

PUBLISHED ONLINE: 2022-04-09

**THERMAL SCIENCE** YEAR

**2022**, VOLUME

**26**, ISSUE

**Issue 2**, PAGES [1037 - 1046]

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