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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