Discontinuous Galerkin Methods for Network Patterning Phase-Field Models

In this paper, we propose a class of discontinuous Galerkin methods under the scalar auxiliary variable framework (SAV-DG) to solve a biological patterning model in the form of parabolic–elliptic partial differential equation system. In particular, mixed-type discontinuous Galerkin approximations ar...

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Bibliographic Details
Published in:Journal of scientific computing 2024, Vol.98 (1), p.27, Article 27
Main Authors: Yang, Lei, Liu, Yuan, Jiang, Yan, Zhang, Mengping
Format: Article
Language:English
Subjects:
Algorithms
Biological models (mathematics)
Computational Mathematics and Numerical Analysis
Energy consumption
Energy dissipation
Finite volume method
Galerkin method
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Partial differential equations
Permeability
Theoretical
Variables
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Summary:In this paper, we propose a class of discontinuous Galerkin methods under the scalar auxiliary variable framework (SAV-DG) to solve a biological patterning model in the form of parabolic–elliptic partial differential equation system. In particular, mixed-type discontinuous Galerkin approximations are used for the spatial discretization, aiming to achieve a balance between the high resolution and computational cost. Second and third order backward differentiation formulas are considered under SAV framework for discrete energy stability. Numerical experiments are provided to show the effectiveness of the fully discrete schemes and the governing factors of patterning formation.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02423-y