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Title: Recovered finite element methods
Authors: Georgoulis, Emmanuil H.
Pryer, Tristan
First Published: 5-Jan-2018
Publisher: Elsevier
Citation: Computer Methods in Applied Mechanics and Engineering, 2018, 332, pp. 303-324
Abstract: We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has a number of attractive features over both classical finite element and discontinuous Galerkin approaches, most important of which is its potential to produce stable conforming approximations in a variety of settings. Moreover, for special choices of recovery operators, R-FEM produces the same approximate solution as the classical conforming finite element method, while, trivially, one can recast (primal formulation) discontinuous Galerkin methods. A priori error bounds are shown for linear second order boundary value problems, verifying the optimality of the proposed method. Residual-type a posteriori bounds are also derived, highlighting the potential of R-FEM in the context of adaptive computations. Numerical experiments highlight the good approximation properties of the method in practice. A discussion on the potential use of R-FEM in various settings is also included.
DOI Link: 10.1016/j.cma.2017.12.026
ISSN: 0045-7825
Embargo on file until: 5-Jan-2020
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © Elsevier, 2018. After an embargo period this version of the paper will be an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description: The file associated with this record is under embargo until 24 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
Appears in Collections:Published Articles, Dept. of Mathematics

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