Computational competition of three adaptive least-squares finite element schemes

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a~posteriori error estimator or an alternative explicit residual-based error estimator as well as a separate marking strategy based on the alternative error estimator and an optimal data approximation algorithm. All three strategies are investigated empirically in this paper for a set of benchmarks examples for the Poisson model problem in two spatial dimensions. Particular interest is on the choice of the marking and refinement parameters and the approximation of the given data.