A space-time finite element method for fractional wave problems

被引:7
|
作者
Li, Binjie [1 ]
Luo, Hao [1 ]
Xie, Xiaoping [1 ]
机构
[1] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China
基金
中国国家自然科学基金;
关键词
Fractional wave problem; Space-time finite element; Convergence; Singularity; Graded grid; DISCONTINUOUS GALERKIN METHOD; NUMERICAL-SOLUTION; DIFFERENCE SCHEME; HP-VERSION; DIFFUSION; SUPERCONVERGENCE; APPROXIMATIONS; EQUATIONS;
D O I
10.1007/s11075-019-00857-w
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we analyze a space-time finite element method for fractional wave problems involving the time fractional derivative of order gamma(1 < gamma < 2). We first establish the stability of the proposed method and then derive the optimal convergence rate in H-1(0, T; L-2(Omega))-norm and suboptimal rate in discrete L-infinity (0, T; H-0(1) (Omega))-norm. Furthermore, we discuss the performance of this method when the true solution has singularity at t = 0 and show that optimal convergence rate with respect to H-1(0, T; L-2(Omega))-norm can still be achieved by using graded temporal grids. Finally, numerical experiments are performed to verify the theoretical results.
引用
收藏
页码:1095 / 1121
页数:27
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