DISCONTINUOUS GALERKIN METHODS FOR WEAKLY COUPLED HYPERBOLIC MULTIDOMAIN PROBLEMS

被引：0

作者：

Liu, Qingyuan ^{[1
]}

Shu, Chi-Wang ^{[2
]}

Zhang, Mengping ^{[1
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2017年 / 39卷 / 05期

基金：

美国国家科学基金会;

关键词：

RKDG scheme; multidomain problems; discontinuous fluxes; biological cell proliferation model; SCALAR CONSERVATION-LAWS; FINITE-ELEMENT-METHOD; STABILITY ANALYSIS; FLUX; APPROXIMATION; EQUATIONS; SELECTION; SCHEMES;

D O I：

10.1137/16M1089332

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop and analyze the Runge-Kutta discontinuous Galerkin (RKDG) method to solve weakly coupled hyperbolic multidomain problems. Such problems involve transfer type boundary conditions with discontinuous fluxes between different domains, calling for special techniques to prove stability of the RKDG methods. We prove both stability and error estimates for our RKDG methods on simple models, and then apply them to a biological cell proliferation model [N. Echenim, D. Monniaux, M. Sorine, and F. Clement, Math. Biosci., 198 (2005), pp. 57-79]. Numerical results are provided to illustrate the good behavior of our RKDG methods.

引用

页码：A2201 / A2230

页数：30

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