The aim of this work is to highlight that the adaptivity of the time step when combined with the adaptivity of the spectral mesh is optimal for a semi-linear parabolic equation discretized by an implicit Euler scheme in time and spectral elements method in space. The numerical results confirm the optimality of the order of convergence. The later is similar to the order of the error indicators.

中文翻译：

---

时间和空间网格对半线性热方程求解的适应性

这项工作的目的是要强调，时间步的适应性与光谱网格的适应性相结合对于半隐式抛物方程是最佳的，该半线性抛物方程由隐式欧拉格式在时间和空间中的光谱元素方法离散化。数值结果证实了收敛阶的最优性。后者类似于错误指示符的顺序。