标题： 具有显式时间积分的波动方程自适应有限元方法 显示英文标题

标题： Adaptive FEM with explicit time integration for the wave equation

摘要： 从最近针对使用显式时间步进的波动方程有限元解的后验误差估计器 [Grote, Lakkis, Santos, 2024] 出发，我们设计了一种时空自适应策略，包括时间演化网格和局部时间步进 [Diaz, Grote, 2009]，以克服由于局部网格细化导致的时间步长过于严格的CFL稳定性限制。此外，在每个时间步中，自适应算法通过误差指示器监控准确性，并在细化网格上重新计算当前步骤，直到满足所需的容差；同时，在误差较小的区域对网格进行粗化。在所有局部网格细化区域应用基于Leapfrog的局部时间步进，以在保留效率的同时将自适应性融入完全显式的时间积分与网格变化中。数值结果说明了后验误差估计器在时间演化网格上的最优收敛率。 显示英文摘要

摘要： Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving meshes and local time-stepping [Diaz, Grote, 2009] to overcome any overly stringent CFL stability restriction on the time-step due to local mesh refinement. Moreover, at each time-step the adaptive algorithm monitors the accuracy thanks to the error indicators and recomputes the current step on a refined mesh until the desired tolerance is met; meanwhile, the mesh is coarsened in regions of smaller errors. Leapfrog based local time-stepping is applied in all regions of local mesh refinement to incorporate adaptivity into fully explicit time integration with mesh change while retaining efficiency. Numerical results illustrate the optimal rate of convergence of the a posteriori error estimators on time evolving meshes.