Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations
Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations
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非线性波动方程节能线性隐式格式的无条件最优收敛
DOI：
10.1007/s11425-020-1857-5
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Zhimin Zhang
中科院分区：
文献类型：
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作者：
Waixiang Cao;Dongfang Li;Zhimin Zhang
本文提出并分析了求解非线性波动方程的一种能量守恒的线性隐格式。在时间上的最优误差估计和在空间上的超收敛误差估计被建立，没有一定的时间步长的限制。其关键是直接估计非线性波动方程和相应的全离散格式在H2范数下的解的界，而以前的研究依赖于时空误差分裂方法.数值算例分别验证了所提出的全离散格式的能量守恒性、无条件收敛性和最优误差估计。
In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions. The key is to estimate directly the solution bounds in theH2-norm for both the nonlinear wave equation and the corresponding fully discrete scheme, while the previous investigations rely on the temporal-spatial error splitting approach. Numerical examples are presented to confirm energy-conserving properties, unconditional convergence and optimal error estimates, respectively, of the proposed fully discrete schemes.