标题： 具有双曲松弛效应的Cahn-Hilliard方程动态边界条件下的首个一阶线性能量稳定格式 显示英文标题

标题： A First-Order Linear Energy Stable Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions under the Effect of Hyperbolic Relaxation

摘要： 本文我们关注带有动态边界条件的Cahn-Hilliard方程，在系统中加入两个双曲松弛项。我们验证了整个系统的能量会随着时间递减。通过加入两个稳定项，我们构建了一个一阶时间精度的数值格式，该格式是线性的并且能量稳定的。然后我们通过误差估计证明了该格式在时间上是一阶精度的。最后我们进行了足够的数值实验以验证该格式的时间收敛性和能量稳定性。此外，我们展示了带和不带双曲项的数值结果的差异，表明双曲项可以帮助总能量缓慢递减。 显示英文摘要

摘要： In this paper we focus on the Cahn-Hilliard equation with dynamic boundary conditions, by adding two hyperbolic relaxation terms to the system. We verify that the energy of the total system is decreasing with time. By adding two stabilization terms, we have constructed a first-order temporal accuracy numerical scheme, which is linear and energy stable. Then we prove that the scheme is of first-order in time by the error estimates. At last we carry out enough numerical results to validate the the temporal convergence and the energy stability of such scheme. Moreover, we have present the differences of the numerical results with and without the hyperbolic terms, which show that the hyperbolic terms can help the total energy decreasing slowly.