In this paper, a linearized energy-stable Galerkin scheme is investigated for a semilinear wave equation. Based on the special property of the bilinear element on the rectangular mesh, the superconvergence error estimate in $L^{\infty }\left(H^1\left(\Omega \right)\right)$ is obtained in terms of a suitable post-processing approach. Finally, a numerical example is presented to support the theoretical analysis.

中文翻译：

---

半线性波动方程的线性化能量稳定Galerkin方案的超收敛误差估计

本文针对半线性波动方程，研究了线性化的能量稳定Galerkin格式。根据矩形网格上双线性元素的特殊性质，估计超收敛误差。${\mathrm{大号}}^{\infty }（H^{\mathrm{1个}}（\Omega ））$根据合适的后处理方法获得。最后，给出一个数值例子来支持理论分析。