Convergence and Optimality of hp-AFEM
نویسندگان
چکیده
We design and analyze an adaptive hp-finite element method (hp-AFEM) in dimensions n = 1, 2. The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy, and REDUCE improves the discrete solution to a finer but comparable accuracy. The former hinges on a recent algorithm by Binev for adaptive hp-approximation, and acts as a coarsening step. We prove convergence and instance optimality.
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