A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes

C. Carstensen, D. Gallistl, J. Hu

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)

Abstract

The discrete reliability of a finite element method is a key ingredient to prove optimal convergence of an adaptive mesh-refinement strategy and requires the interchange of a coarse triangulation and some arbitrary refinement of it. One approach for this is the careful design of an intermediate triangulation with one-level refinements and with the remaining difficulty to design some interpolation operator which maps a possibly nonconforming approximation into the finite element space based on the finer triangulation. This paper enfolds the second possibility of some novel discrete Helmholtz decomposition for the nonconforming Morley finite element method. This guarantees the optimality of a standard adaptive mesh-refining algorithm for the biharmonic equation. Numerical examples illustrate the crucial dependence of the bulk parameter and the surprisingly short pre-asymptotic range of the adaptive Morley finite element method.
Original languageEnglish
Pages (from-to)2167-2181
Number of pages15
JournalComputers and mathematics with applications
Volume68
Issue number12, Part B
DOIs
Publication statusPublished - 2014
Externally publishedYes

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