可压缩Navier-斯托克斯方程有限元/有限体积混合格式的一致性、收敛性和误差估计
Consistency, convergence and error estimates for a mixed finite element / finite volume scheme to compressible Navier-Stokes equations with general inflow/outflow boundary data
摘要：
对于一般非零流入/流出边界条件的问题，在绝热系数γ的全范围内，研究了等熵区可压缩Navier斯托克斯方程的混合有限元-有限体积格式的收敛性。我们提出了一个修改的Karper计划[Numer. 125：441-510，2013]，以适应非零边界数据，证明其解的存在性，建立稳定性和一致性估计，推导平衡定律的方便一致性公式，并使用它来显示数值解到具有Abbatiello等人[预印本Arxiv 1912.12896]中引入的Elderold缺陷的耗散解的弱收敛。如果目标系统存在一个强解，则收敛到该强解。此外，我们建立了强收敛的收敛速度的大小的空间离散h（这是假设是可比的时间步长）。在非零流入/流出边界数据的情况下，所有结果都是新的。后者的结果也是新的无滑移边界条件。
英文摘要：
We study convergence of a mixed finite element-finite volume scheme for the compressible Navier Stokes equations in the isentropic regime under the full range of the adiabatic coefficient gamma for the problem with general non zero inflow/outflow boundary conditions. We propose a modification of Karper scheme [Numer. Math. 125:441-510, 2013] in order to accommodate the non zero boundary data, prove existence of its solutions, establish the stability and uniform estimates, derive a convenient consistency formulation of the balance laws and use it to show the weak convergence of the numerical solutions to a dissipative solution with the Reynold defect introduced in Abbatiello et al. [Preprint Arxiv 1912.12896]. If the target system admits a strong solution then the convergence is strong towards the strong solution. Moreover, we establish the convergence rate of the strong convergence in terms of the size of the space discretization h (which is supposed to be comparable with the time step). In the case of non zero inflow/outflow boundary data, all results are new. The latter result is new also for the no-slip boundary conditions.
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