A fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed form. (English) Zbl 07678426
Summary: In this paper, we develop a fully discrete virtual element scheme for the Cahn-Hilliard problem in mixed form. The discrete system, derived by combining the convex splitting technique and a virtual element discrete nonlinear term different from that of Antonietti et al. (2016), Liu and Chen (2019) not only exhibits the unconditional unique solvability and the effectiveness of the large time step size, but also possesses the mass conservation and a discrete energy decaying property. Moreover, the proposed scheme supports arbitrary polygons (including non-convex elements) and arbitrary approximation orders. By following the algebraic implementation of the discrete system, we investigate several numerical experiments to present the performance of this numerical scheme.
Keywords:
Cahn-Hilliard problem; mixed formulation; virtual element method; essential properties; algebraic implementationReferences:
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