Convergence Theory of Adaptive Mixed Finite Element Methods for the Stokes Problem

We establish a conditional optimality result for an adaptive mixed finite element method for the stationary Stokes problem discretized by the standard Taylor–Hood elements under the assumption of the so-called general quasiorthogonality. Optimality is measured in terms of a modified approximation class defined through the total error. We prove that the modified approximation class coincides with the standard approximation class, modulo the assumption that the data is regular enough in an appropriate scale of Besov spaces.