论文标题
压力稳定误差估计的最佳阶阶在具有边缘的域上的stokes方程
Pressure-robust error estimate of optimal order for the Stokes equations on domains with edges
论文作者
论文摘要
不可压缩的Stokes方程的速度解决方案不受右侧数据形式的变化的影响。大多数混合方法由于放松的差异约束而在离散公式中不复制此属性，这意味着它们不是压力的。经典方法的最新重建方法通过将离散无差异测试功能映射到$ \ boldsymbol {h}（h \ propatatOrnArname {div}）$的意义上，从而恢复了离散解决方案的这种不变性属性。此外，Stokes解决方案在凹面边缘附近的三维结构域中具有局部奇异的行为，从而降低了准均匀网格上的收敛速率，并使各向异性网格分级合理，以恢复最佳收敛特性。使用重建方法显示了针对压力射击修改的Crouzeix-raviart方法，显示了具有适当各向异性分级的张量产物类型网格上最佳顺序的有限元误差估计。数值示例支持理论结果。
The velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields. Most mixed methods do not replicate this property in the discrete formulation due to a relaxation of the divergence constraint which means that they are not pressure-robust. A recent reconstruction approach for classical methods recovers this invariance property for the discrete solution, by mapping discretely divergence-free test functions to exactly divergence-free functions in the sense of $\boldsymbol{H}(\operatorname{div})$. Moreover, the Stokes solution has locally singular behavior in three-dimensional domains near concave edges, which degrades the convergence rates on quasi-uniform meshes and makes anisotropic mesh grading reasonable in order to regain optimal convergence characteristics. Finite element error estimates of optimal order on meshes of tensor-product type with appropriate anisotropic grading are shown for the pressure-robust modified Crouzeix--Raviart method using the reconstruction approach. Numerical examples support the theoretical results.
