A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal component penalty terms to cancel out the pressure term. Consequently, the Stokes equation can be solved as an elliptic system instead of a saddle-point problem due to such weak form. The number of degree of freedoms of our method is the same as the number of elements in the mesh for different order of accuracy. The error estimations of the proposed method are given in a classical style, which are then verified by some numerical examples.

中文翻译：

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基于无散度块重建的斯托克斯方程的不连续伽辽金方法

针对斯托克斯流，提出了一种通过补丁重建的不连续伽辽金方法。采用局部无发散重构空间作为逼近空间，采用内部惩罚法，施加法向分量惩罚项抵消压力项。因此，由于这种弱形式，斯托克斯方程可以求解为椭圆系统而不是鞍点问题。我们方法的自由度数与网格中不同精度顺序的元素数相同。所提出方法的误差估计以经典风格给出，然后通过一些数值例子进行验证。