发表机构
Saarland University; Karlsruhe Institute of Technology（萨尔大学; 卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种结合蛙跳与Crank--Nicolson的显式二阶格式，用于解耦波-热耦合系统，仅受双曲CFL条件约束，并通过数值实验验证了误差估计。
AI 中文摘要
本文提出并分析了一种用于耦合波-热系统的数值方法，该系统出现在例如具有记忆的粘弹性、具有有限热速度的热弹性波传播以及耦合到色散材料定律的麦克斯韦方程组中。鉴于显式蛙跳格式在波动问题中的广泛使用以及热方程对抛物型时间步长的限制，我们设计了一种二阶格式，该格式将波动部分的蛙跳时间积分与热部分的Crank--Nicolson步相结合。耦合以Strang分裂方式安排，使得整体格式在耦合中保持显式，并且仅受双曲型CFL条件约束，而非更严格的抛物型约束。我们引入了一种抽象空间离散化，它涵盖了一大类波-热系统，并适用于协调和非协调稳定化离散。利用一般误差分解，我们在期望的CFL条件下推导了全离散格式的误差估计。针对我们模型应用的数值实验证实了理论结果。
英文摘要
This paper proposes and analyzes a numerical method for coupled wave-heat systems that arise, for example, in visco-elasticity with memory, thermo-elastic wave propagation with finite thermal speed, and Maxwell's equations coupled to dispersive material laws. Motivated by the widespread use of explicit leapfrog schemes for wave problems and the parabolic time-step restriction for heat equations, we design a second-order scheme that combines leapfrog time integration for the wave part with a Crank--Nicolson step for the heat part. The coupling is arranged in a Strang-splitting--type fashion so that the overall scheme remains explicit in the coupling and is subject only to a CFL condition of hyperbolic type, rather than the more restrictive parabolic constraint. We introduce an abstract space discretization that covers a broad class of wave--heat systems and accommodates both conforming and stabilized non-conforming discretizations. Using a general error decomposition, we derive error estimates for the fully discrete scheme under the desired CFL condition. Numerical experiments for our model applications confirm the theoretical results.
Comments49 pages, 8 figures
