论文标题
在多面眼网上符合Stokes问题的不连续的Galerkin有限元法
A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes
论文作者
论文摘要
在主要速度压力公式中开发了一种新的Stokes方程的不连续的Galerkin有限元方法。该方法采用不连续的多项式来实现一般多边形/多面体网格的速度和压力。大多数具有不连续近似的有限元方法具有一个或多个稳定术语的速度和保证稳定性和收敛性的压力。这种新的有限元方法具有标准的有限元公式，而没有任何速度或压力稳定器。在各种规范中为相应的数值近似建立了最佳订单误差估计。测试了数值示例的低和高阶元素，直到2D和3D空间中的4度。
A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general polygonal/polyhedral meshes. Most finite element methods with discontinuous approximation have one or more stabilizing terms for velocity and for pressure to guarantee stability and convergence. This new finite element method has the standard conforming finite element formulation, without any velocity or pressure stabilizers. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. The numerical examples are tested for low and high order elements up to the degree four in 2D and 3D spaces.
