We design and analyze an adaptive hp-finite element method ((Formula presented.)-AFEM) in dimensions (Formula presented.). The algorithm consists of iterating two routines: (Formula presented.)-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.

Convergence and optimality of hp-AFEM

VERANI, MARCO
2017-01-01

Abstract

We design and analyze an adaptive hp-finite element method ((Formula presented.)-AFEM) in dimensions (Formula presented.). The algorithm consists of iterating two routines: (Formula presented.)-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.
2017
Applied Mathematics; Computational Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1002744
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