论文标题
混合有限元 /有限体积方案的一致性，收敛性和误差估计，可压缩通用流入 /流出边界数据的Navier-Stokes方程
Consistency, convergence and error estimates for a mixed finite element / finite volume scheme to compressible Navier-Stokes equations with general inflow/outflow boundary data
论文作者
论文摘要
我们研究了在绝热系数伽玛的全部范围内，对于一般非零流入/流出边界条件的问题，在整个绝热系数伽玛的范围内，在等等方面的可压缩纳维尔方程的混合有限元元素体积方案的收敛性。我们提出了karper方案的修改[numer。数学。 125：441-510，2013]为了适应非零边界数据，证明其解决方案的存在，建立稳定性和统一的估计，得出了平衡法律的便利一致性表述，并使用它来显示数值解决方案与Reynold Defect te abbatiello in in Abbatiello Al Al al Al Al Al Al and abbatiellos and abbatielly and abbatiell and abbatiell and abbatiel and abteral的差异。 [Preprint Arxiv 1912.12896]。如果目标系统允许强大的解决方案，那么收敛性对强溶液的强大。此外，我们根据空间离散化h的大小（应该与时间步长相当），建立了强收敛的收敛速率。在非零流入/流出边界数据的情况下，所有结果都是新的。后一个结果也是新的防滑边界条件的新结果。
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.
