论文标题
渐近无恒定和多项式 - 射击量的后验估计值，用于波动方程的空间离散化
Asymptotically constant-free and polynomial-degree-robust a posteriori estimates for space discretizations of the wave equation
论文作者
论文摘要
我们通过有限元素得出了标量波方程空间（半离散）的后验误差估计器。在理想化的设置中，忽略时间离散化且模拟时间很长，我们提供了完全保证的上限，这些上限是渐进的恒定不恒定的，并表明所提出的估计器是有效的，多项式的量子，这意味着效率常数不会随着近似顺序的增加而降低效率常数。据我们所知，这项工作是首次获得波动方程的有效误差估计的工作。我们还可以在没有分析的情况下解释估计器如何通过明确的时间集成方案来弥补时间离散化。数值示例说明了理论，并表明它是锋利的。
We derive an equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. In the idealized setting where time discretization is ignored and the simulation time is large, we provide fully-guaranteed upper bounds that are asymptotically constant-free and show that the proposed estimator is efficient and polynomial-degree-robust, meaning that the efficiency constant does not deteriorate as the approximation order is increased. To the best of our knowledge, this work is the first to derive provably efficient error estimates for the wave equation. We also explain, without analysis, how the estimator is adapted to cover time discretization by an explicit time integration scheme. Numerical examples illustrate the theory and suggest that it is sharp.
