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 \({\varvec{H}}({\text {div}})\). 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.

不可压缩的斯托克斯方程的速度解不受梯度场形式的右侧数据变化的影响。由于分散约束的放松，大多数混合方法无法在离散配方中复制此特性，这意味着它们不耐压力。通过将离散无散度测试函数映射到\（{\ varvec {H}}（{\ text {div} }）\）。此外，Stokes解在凹边附近的三维域中具有局部奇异行为，这降低了准均匀网格上的收敛速度，并使各向异性网格渐变合理以恢复最佳收敛特性。使用重构方法，对压力鲁棒性改进的Crouzeix-Raviart方法显示了张量积类型且具有适当各向异性渐变的网格上最佳阶的有限元误差估计。数值例子支持了理论结果。