An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave equation

被引：21
作者：
Joly, P [1 ]
Rodríguez, J [1 ]
机构：
[1] INRIA Rocquencourt, Le Chesnay, France
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2005年 / 43卷 / 02期
关键词：
mesh refinement; local time stepping; error estimates; stability; energy conservation; wave equation;
D O I：
10.1137/040603437
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study two space-time mesh refinement methods as the one introduced in [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 197-221]. The stability of such methods is guaranteed by construction through the conservation of a discrete energy. In this paper, we show the L-2 convergence of these schemes and provide optimal error estimates. The proof is based on energy techniques and bootstrap arguments. Our results are validated with numerical simulations and compared with results from plane wave analysis [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 223-251].
引用
收藏
页码：825 / 859
页数：35
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