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.

中文翻译：

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多面网格上斯托克斯问题的符合非连续伽辽金有限元方法

在初级速度-压力公式中开发了一种新的用于斯托克斯方程的非连续伽辽金有限元方法。此方法对一般多边形/多面体网格上的速度和压力均采用不连续多项式。大多数具有不连续近似的有限元方法具有一个或多个速度和压力稳定项，以保证稳定性和收敛性。这种新的有限元方法具有符合标准的有限元公式，没有任何速度或压力稳定器。为各种范数中的相应数值近似建立了最优阶误差估计。数值示例针对 2D 和 3D 空间中高达四阶的低阶和高阶元素进行了测试。