论文标题
稳定性分析Stokes问题的多重不连续的盖尔金近似值与流体结构相互作用问题的应用
Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems
论文作者
论文摘要
我们在多面部和多面部网格（Polydg）上对Stokes问题进行了不连续的Galerkin方法的稳定分析。特别是，我们分析了离散的INF-SUP条件，以实现速度和压力近似空间的多项式近似顺序的不同选择。为此，我们采用了具有压力稳定项的广义INF-SUP条件。我们还证明了合适规范中的先验HP-version误差估计。我们从数值上检查INF-SUP常数的行为以及相对于网格配置，网格大小和多项式程度的收敛顺序。最后，作为我们分析的相关应用，我们考虑了流体结构相互作用问题的PolyDG近似，并且我们从数值探索了该方法的稳定性属性。
We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial approximation order of the velocity and pressure approximation spaces. To this aim, we employ a generalized inf-sup condition with a pressure stabilization term. We also prove a priori hp-version error estimates in suitable norms. We numerically check the behaviour of the inf-sup constant and the order of convergence with respect to the mesh configuration, the mesh-size, and the polynomial degree. Finally, as a relevant application of our analysis, we consider the PolyDG approximation for a fluid-structure interaction problem and we numerically explore the stability properties of the method.
