Convergence and optimality of hp-AFEM
| Authors |
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|---|---|
| Publication date | 2017 |
| Journal | Numerische Mathematik |
| Volume | Issue number | 135 | 4 |
| Pages (from-to) | 1073-1119 |
| Organisations |
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| Abstract | 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. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1007/s00211-016-0826-x |
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