Space-time adaptive methods for the pseudostress formulation of the Stokes problem

Abstract In this paper, we are concerned with a posteriori error analysis for fully discrete solutions for the pseudostress-velocity formulation of the time dependent Stokes problem including nonhomogeneous mixed boundary conditions. The pseudostress-velocity formulation of the Stokes problem allows Raviart–Thomas finite elements. Piecewise constant discontinuous Galerkin method in time is proposed so that mixed finite element spaces are permitted to change at different time levels. Space-time a posteriori error estimates are derived by exploiting the residual and error representation formula in combination with the Stokes dual problem. Based on these estimates, we propose an adaptive space-time algorithm (ASTA), which includes features such as a space-time mesh change indicator and the separation of space error indicators from time error indicators. Numerical results highlight the superior efficiency of ASTA compared to uniform meshes. Additionally, our algorithm is able to effectively capture the corner singularity of the pressure variable in the backward-facing step flow problem.