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Recovered finite element methods

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journal contribution
posted on 2018-05-10, 09:00 authored by Emmanuil H. Georgoulis, Tristan Pryer
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.

History

Citation

Computer Methods in Applied Mechanics and Engineering, 2018, 332, pp. 303-324

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

Computer Methods in Applied Mechanics and Engineering

Publisher

Elsevier

issn

0045-7825

Acceptance date

2017-12-20

Copyright date

2018

Publisher version

https://www.sciencedirect.com/science/article/pii/S0045782517307764?via=ihub

Notes

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.

Language

en

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