A stabilized hybrid discontinuous Galerkin method for the Cahn-Hilliard equation
Medina, Emmanuel Y. Y. 1Toledo, Elson M. M. 1Igreja, Iury 1Rocha, Bernardo M. M.1
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作者信息
1. Univ Fed Juiz de Fora
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Abstract
In this paper, we present a stabilized mixed hybrid discontinuous Galerkin finite element method for solving fourth-order parabolic problems such as the Cahn-Hilliard equation used to describe the dynamics of avascular tumor growth. The proposed method is compared to other methods previously studied in this context. Several numerical experiments are presented to show convergence, performance and accuracy comparisons with other methods. Besides, we also show the ability of the method to solve a complex case of avascular tumor growth where the behavior of tumor cells towards nutrient gradients drives fingering instabilities. The results show the great potential of the presented method for the efficient and accurate solution of Cahn-Hilliard problems which includes applications on complex tumor growth problems. (c) 2021 Elsevier B.V. All rights reserved.
Key words
Cahn-Hilliard/Finite element method/Hybridizable discontinuous Galerkin/Tumor growth modeling/FINITE-ELEMENT METHODS/TUMOR-GROWTH/INTERIOR PENALTY/ENERGY/MODEL/DGFEM
NSTL
Elsevier