Saturation and reliable hierarchical a posteriori Morley finite element error control

C. Carstensen, D. Gallistl, Y. Huang

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    This paper proves the saturation assumption for the nonconforming Morley finite element discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is strictly reduced by a contraction factor smaller than one up to explicit higher-order data approximation terms. The refinement has at least to bisect any edge such as red refinement or 3-bisections on any triangle.

    This justifies a hierarchical error estimator for the Morley finite element method, which simply compares the discrete solutions of one mesh and its red-refinement. The related adaptive mesh-refining strategy performs optimally in numerical experiments. A remark for Crouzeix-Raviart nonconforming finite element error control is included.
    Original languageEnglish
    Pages (from-to)833-844
    Number of pages12
    JournalJournal of Computational Mathematics
    Volume36
    Issue number6
    DOIs
    Publication statusPublished - 2018

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