A C1 VIRTUAL ELEMENT METHOD FOR THE CAHN-HILLIARD EQUATION WITH POLYGONAL MESHES

被引：187

作者：

Antonietti, P. F. ^{[1
]}

Da Veiga, L. Beirao ^{[2
]}

Scacchi, S. ^{[3
]}

Verani, M. ^{[1
,4
]}

机构：

[1] Politecn Milan, MOX Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 53, I-20125 Milan, Italy

[3] Univ Milan, Dipartimento Matemat, Via Saldini 50, I-20133 Milan, Italy

[4] CNR, Ist Matemat Applicata & Tecnol Informat E Magenes, Via Ferrata 1, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 01期

关键词：

virtual element method; Cahn-Hilliard equation; FINITE-ELEMENTS; TUMOR-GROWTH; ERROR; MODEL; APPROXIMATION; FORMULATION; SEPARATION;

D O I：

10.1137/15M1008117

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：34 / 56

页数：23

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