Virtual element method for semilinear hyperbolic problems on polygonal meshes

被引:26
|
作者
Adak, Dibyendu [1 ]
Natarajan, E. [1 ]
Kumar, Sarvesh [1 ]
机构
[1] Indian Inst Space Sci & Technol, Dept Math, Thiruvananthapuram, Kerala, India
关键词
Virtual element method; polygonal meshes; Newmark scheme; conforming methods; error estimates; numerical experiments; STOKES PROBLEM; MIMETIC DISCRETIZATION; ELLIPTIC PROBLEMS; EQUATION; ORDER;
D O I
10.1080/00207160.2018.1475651
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This article deals with the development of the virtual element method for the approximation of semilinear hyperbolic problems. For the space discretization, two different operators are used: the energy projection operator and an internal -projection operator . In order to deal with the time derivative, a Newmark scheme is employed; and the resulted fully discrete scheme is analysed. Moreover, with the help of projection operators, optimal error estimates are derived for both semi- and fully discrete schemes in -norm and -norm. We have conducted numerical experiments on polygonal meshes to illustrate the performance of the proposed scheme and validate the theoretical findings.
引用
收藏
页码:971 / 991
页数:21
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