Recovered Finite Element Methods

Emmanuil H. Georgoulis, Tristan Pryer

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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.
Original languageEnglish
Pages (from-to)303-324
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Early online date5 Jan 2018
Publication statusPublished - 15 Apr 2018

Bibliographical note

25 pages, 10 figures


  • math.NA


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