Recent theoretical results are discussed for the key components needed for an adaptive hp-version finite element algorithm, including a reliable and efficient a posteriori error estimator; an adaptive hp-refinement strategy, and, efficient solvers for the large, ill-conditioned systems of linear equations. Together, these provide the basis 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 performance of the whole algorithm is illustrated for some standard benchmark problems taken from linear elasticity.

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1996-1997 Mathematics in High Performance Computing