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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多面体网格上Stokes问题的一致不连续Galerkin有限元方法

在一次速度-压力公式中，开发了一种新的不连续的Galerkin有限元方法来处理Stokes方程。该方法对一般的多边形/多面体网格上的速度和压力采用不连续的多项式。大多数具有不连续逼近的有限元方法都具有一个或多个关于速度和压力的稳定项，以确保稳定性和收敛性。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。为各种规范中的相应数值近似建立了最佳阶误差估计。在2D和3D空间中，对数值示例进行了高达4级的低阶和高阶元素的测试。