Discontinuous Galerkin Methods for Network Patterning Phase-Field Models

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Authors
Yang, Lei
Liu, Yuan
Jiang, Yan
Zhang, Mengping
Issue Date
2023-12
Type
Article
Language
en-US
Keywords
Biological network patterning , Discontinuous Galerkin , Scalar auxiliary variable , Backward difference formula
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Abstract

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.

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Yang, L., Liu, Y., Jiang, Y., & Zhang, M. (2023). Discontinuous Galerkin Methods for Network Patterning Phase-Field Models. Journal of Scientific Computing, vol. 98, no.1, art. no. 27. https://doi.org/10.1007/s10915-023-02423-y
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Springer
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ISSN
0885-7474
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