论文标题
一种新的DG方法，用于用强对称性的Brinkman问题进行纯压力。
A new DG method for a pure--stress formulation of the Brinkman problem with strong symmetry
论文作者
论文摘要
对于具有混合边界条件的边界方程提出了强烈的对称应力近似。所得的配方使用对称内部惩罚不连续的盖尔金方法解决了考克（Cauchy）应力。压力和速度很容易从应力后进行后期加工，并且证明第二个后处理能够产生完全无差异的离散速度。我们证明了该方法在DG-能量规范方面的稳定性，并获得有关问题系数明确的误差估计值。我们得出应力和后处理变量的最佳收敛速率。此外，在网格上的适当假设下，我们证明了压力的最佳$ l^2 $ eRROR估计。最后，我们提供2D和3D的数值示例。
A strongly symmetric stress approximation is proposed for the Brinkman equations with mixed boundary conditions. The resulting formulation solves for the Cauchy stress using a symmetric interior penalty discontinuous Galerkin method. Pressure and velocity are readily post-processed from stress, and a second post-process is shown to produce exactly divergence-free discrete velocities. We demonstrate the stability of the method with respect to a DG-energy norm and obtain error estimates that are explicit with respect to the coefficients of the problem. We derive optimal rates of convergence for the stress and for the post-processed variables. Moreover, under appropriate assumptions on the mesh, we prove optimal $L^2$-error estimates for the stress. Finally, we provide numerical examples in 2D and 3D.
