Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S677 - S704|
|Published online||26 February 2021|
General polytopal H(div)-conformal finite elements and their discretisation spaces
Institute of Mathematics, University of Zurich, 8057 Zurich, Switzerland
* Corresponding author: firstname.lastname@example.org
Accepted: 18 July 2020
We present a class of discretisation spaces and H(div)-conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the element’s shape with the divergence properties of the Raviart–Thomas elements on the boundaries, the designed frameworks offer a wide range of H(div)-conformal discretisations. As those elements are set up through degrees of freedom, their definitions are easily amenable to the properties the approximated quantities are wished to fulfil. Furthermore, we show that one straightforward restriction of this general setting share its properties with the classical Raviart–Thomas elements at each interface, for any order and any polytopal shape. Then, to close the introduction of those new elements by an example, we investigate the shape of the basis functions corresponding to particular elements in the two dimensional case.
Mathematics Subject Classification: 65N30
Key words: H(div)-conformity / finite elements / Raviart–Thomas elements / polytopal elements
© EDP Sciences, SMAI 2021
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