Error estimates for well-balanced and time-split schemes on a damped semilinear wave equation
Error estimates for well-balanced and time-split schemes on a damped semilinear wave equation
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阻尼半线性波动方程的良好平衡和时分格式的误差估计
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. J−∗−
中科院分区：
文献类型：
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作者：
D. Amadori;L. Gosse;J. J−∗−
． 对于一维半线性阻尼波动方程的柯西问题唯一弱解的平衡（WB）和分数步（FS）数值近似，导出了后测l1误差估计（在[15,26]意义上）。为了建立WB算法，我们将其改写为线性对流结构允许的初等3 × 3系统的形式，将具有最优Courant数的Godunov格式（对应∆t =∆x）简化为不需要投影到分段常数函数上的任何步骤的波前跟踪算法。证明了总变差估计的根本差异，这部分解释了当耗散（汇）项在空间变量中显示显式依赖时FS方法的差异。采用线性阻尼波动方程的平稳精确解进行了数值试验。
. A posteriori L 1 error estimates (in the sense of [15, 26]) are derived for both well-balanced (WB) and fractional-step (FS) numerical approximations of the unique weak solution of the Cauchy problem for the 1D semilinear damped wave equation. For setting up the WB algorithm, we proceed by rewriting it under the form of an elementary 3 × 3 system which linear convective structure allows to reduce the Godunov scheme with optimal Courant number (corresponding to ∆ t = ∆ x ) to a wavefront-tracking algorithm free from any step of projection onto piecewise constant functions. A fundamental difference in the total variation estimates is proved, which partly explains the discrepancy of the FS method when the dissipative (sink) term displays an explicit dependence in the space variable. Numerical tests are performed by means of stationary exact solutions of the linear damped wave equation.