Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations (Q2044142)

In this article, the authors derive a posteriori and a priori error estimates for the Stokes equation in 2D and 3D domains. Here, the major difficulty is the handling of the divergence-free condition. To overcome this challenge, they use the hypercircle method along with the Scott-Vogelius finite element scheme. Further, they apply the a priori error estimation to the eigenvalue estimation problem for the Stokes operator. Finally, some numerical simulations are performed to show the efficiency of the proposed numerical scheme.