A C1 Virtual Element Method for the Cahn-Hilliard Equation with Polygonal Meshes

作者：P. Antonietti, L. Veiga, S. Scacchi, M. Verani · 发表于：SIAM Journal on Numerical Analysis · 年份：2015 · DOI：10.1137/15m1008117 · 被引用次数：238 · 研究领域：Mathematics、Computer Science

In this paper we develop an evolution of the $C^1$ virtual elements of minimal degree for the approximation of the Cahn--Hilliard equation. The proposed method has the advantage of being conforming in $H^2$ and making use of a very simple set of degrees of freedom, namely, 3 degrees of freedom per vertex of the mesh. Moreover, although the present method is new also on triangles, it can make use of general polygonal meshes. As a theoretical and practical support, we prove the convergence of the semidiscrete scheme and investigate the performance of the fully discrete scheme through a set of numerical tests.