论文标题
完全离散的松散耦合的robin-robin方案，用于不可压缩的流体结构相互作用：稳定性和误差分析
Fully discrete loosely coupled Robin-Robin scheme for incompressible fluid-structure interaction: stability and error analysis
论文作者
论文摘要
我们考虑了一种基于{\ emph {[Burman，durst \＆Guzmán，arxiv：1911.06760]}}的时间半混凝土分裂方法的不可压缩流体结构相互作用的完全离散的方案。分散方法使用罗宾 - 罗宾类型的耦合，该耦合允许固体和流体系统的分离解决方案，而无需内部迭代。对于空间的离散化，我们考虑所有领域的分段仿射连续有限元素，并通过使用Brezizi-Pitkäranta型压力稳定来确保INF-SUP条件。界面流体压力以一种一致的方式进行评估，这表明可以接受等效的Lagrange乘数公式。我们证明该方法无条件地稳定并且相对于系统中的添加质量量而言。此外，我们提供了一个错误估算，该错误估算显示了系统的自然能量规范的错误是$ \ Mathcal o \ big（\ sqrt {t}（\ sqrt {\ sqrt {Δt} + h）\ big）$ t $，其中$ t $是最终的时间，$δT$ $δT$ time-Δt$ time-Δt$ time-Δ
We consider a fully discrete loosely coupled scheme for incompressible fluid-structure interaction based on the time semi-discrete splitting method introduced in {\emph{[Burman, Durst \& Guzmán, arXiv:1911.06760]}}. The splittling method uses a Robin-Robin type coupling that allows for a segregated solution of the solid and the fluid systems, without inner iterations. For the discretisation in space we consider piecewise affine continuous finite elements for all the fields and ensure the inf-sup condition by using a Brezzi-Pitkäranta type pressure stabilization. The interfacial fluid-stresses are evaluated in a variationally consistent fashion, that is shown to admit an equivalent Lagrange multiplier formulation. We prove that the method is unconditionally stable and robust with respect to the amount of added-mass in the system. Furthermore, we provide an error estimate that shows the error in the natural energy norm for the system is $\mathcal O\big(\sqrt{T}(\sqrt{Δt} + h)\big)$ where $T$ is the final time, $Δt$ the time-step length and $h$ the space discretization parameter.
