Aspects of an adaptive hp-finite element method: Adaptive strategy, conforming approximation and efficient solvers

The main components needed far an adaptive hp-version finite element algorithm are discussed: an adaptive hp-refinement strategy, effective methods for constructing conforming hp-approximations, and, efficient solvers for the large, ill-conditioned systems of linear equations. Together, these provide the methodology for an effective adaptive hp-version algorithm. The presentation emphasizes the links between the differing components showing how the algorithms may be implemented efficiently in practice. The main principles are illustrated by use of concrete examples so that a non-expert may develop their own adaptive hp-code. The performance of the whole algorithm is illustrated for some representative problems taken from linear elasticity.