Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis

Abstract In two dimensions, we propose and analyse an iterative a posteriori error indicator for the discontinuous Galerkin finite element approximations of the Stokes equations under boundary conditions of friction type. Two sources of error are identified here, namely; the discretisation error and the linearization error. Under a smallness assumption on data, we prove that the devised error estimator is reliable. Balancing these two errors is crucial to design an adaptive strategy for mesh refinement. We illustrate the theory with some representative numerical examples.