Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation (Q1934460)

The paper concerns the convergence and complexity of adaptive mixed finite element methods (FEMs) for the Poisson equation. The analysis starts with the proof of a quasi-orthogonality result and a localized upper bound for the error of nested discrete solutions. Then the authors prove an error estimate for an adaptive FEM based on the the quasi-orthogonality. Finally, the complexity is obtained using the a posteriori error estimates for the mixed FEM. The authors claim that the results can be extended to the 3D case if the argument for the discrete reliability, i.e., a local stable projection operator associated with two nested edge element spaces and a localized regular decomposition, for time-harmonic Maxwell's equations is employed.