论文标题
对Stokes流量系统的不连续不连续的Galerkin方法的相等高阶分析
Equal higher order analysis of an unfitted discontinuous Galerkin method for Stokes flow systems
论文作者
论文摘要
在这项工作中，我们分析了基于相等的高阶不连续速度和压力的Stokes系统的数值解决方案的不连续的Galerkin离散化。这种方法结合了两个世界的最好的，首先是一部分不连续的高阶准确近似的优势，其次是一个不符合到可能复杂的物体和/或几何变形的真实几何网格的优势。利用虚构的域框架，感兴趣的物理领域嵌入了未固定的背景网格中，几何未固定的离散化建立在对称内部惩罚不连续的Galerkin公式之上。为了提高稳定性，我们用压力稳定项丰富了离散的变分配方。此外，目前的贡献采用了高级幽灵惩罚策略，以解决由不固定边界的小截断元素引起的系统矩阵的不良调节。由连续未固定的FEM [21,74,75]以及其他未固定的网状调查的动机，该调查基于不连续的空间[10,44,45,73]，我们使用适当的速度和压力幽灵惩罚在切割细胞的面上定义，以建立一种强大的高阶方法，以良好的高阶方法建立了一种通常在DG方法上的细胞Agrogomeration技术。当前的演示文稿应证明在工程应用中有价值，在这些应用程序上，特别重点是达到最佳的有效近似，从而在更粗糙的网格中获得相对误差要小得多。研究了INF-SUP稳定性，最佳收敛顺序以及相对于切割配置的条件数敏感性。数值示例验证理论结果。
In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds, firstly the advantages of a piece-wise discontinuous high-order accurate approximation and secondly the advantages of an unfitted to the true geometry grid around possibly complex objects and/or geometrical deformations. Utilizing a fictitious domain framework, the physical domain of interest is embedded in an unfitted background mesh and the geometrically unfitted discretization is built upon symmetric interior penalty discontinuous Galerkin formulation. To enhance stability we enrich the discrete variational formulation with a pressure stabilization term. Moreover, the present contribution adopts high order ghost penalty strategies to address the ill conditioning of the system matrix caused by small truncated elements with respect to the unfitted boundary. Motivated by continuous unfitted FEM [21,74,75] along with other unfitted mesh surveys grounded on discontinuous spaces [10,44,45,73], we use proper velocity and pressure ghost penalties defined on faces of cut cells to establish a robust high-order method, in spite of the cell agglomeration technique usually applied on dG methods. The current presentation should prove valuable in engineering applications where special emphasis is placed on the optimal effective approximation attaining much smaller relative errors in coarser meshes. Inf-sup stability, the optimal order of convergence, and the condition number sensitivity with respect to cut configuration are investigated. Numerical examples verify the theoretical results.
