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An implicit–explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions
Numerische Mathematik ( IF 2.1 ) Pub Date : 2021-03-03 , DOI: 10.1007/s00211-021-01184-w
Marlis Hochbruck , Jan Leibold

We construct and analyze a second-order implicit–explicit (IMEX) scheme for the time integration of semilinear second-order wave equations. The scheme treats the stiff linear part of the problem implicitly and the nonlinear part explicitly. This makes the scheme unconditionally stable and at the same time very efficient, since it only requires the solution of one linear system of equations per time step. For the combination of the IMEX scheme with a general, abstract, nonconforming space discretization we prove a full discretization error bound. We then apply the method to a nonconforming finite element discretization of an acoustic wave equation with a kinetic boundary condition. This yields a fully discrete scheme and a corresponding a-priori error estimate.



中文翻译:

二阶半线性波动方程的隐式-显式时间离散化方案及其在动态边界条件下的应用

我们为半线性二阶波动方程的时间积分构造并分析了二阶隐式显式(IMEX)方案。该方案隐式地处理问题的刚性线性部分,而显式地处理非线性部分。这使得该方案无条件地稳定并且同时非常有效,因为它仅需要在每个时间步上求解一个线性方程组。对于IMEX方案与一般的,抽象的,不一致的空间离散化的组合,我们证明了完全离散化误差范围。然后,我们将该方法应用于具有动力学边界条件的声波方程的非协调有限元离散化。这产生了完全离散的方案和相应的先验误差估计。

更新日期:2021-03-04
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