General polytopal H(div)-conformal finite elements and their discretisation spaces
| Autor: | Rémi Abgrall, Philipp Öffner, Élise Le Mélédo |
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| Přispěvatelé: | University of Zurich, Le Mélédo, Élise |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Discretization 340 Law Conformal map Polytope Basis function 610 Medicine & health 010103 numerical & computational mathematics 01 natural sciences 510 Mathematics 2604 Applied Mathematics Modelling and Simulation 0101 mathematics 2612 Numerical Analysis Mathematics Numerical Analysis Applied Mathematics Degrees of freedom 2603 Analysis Finite element method 010101 applied mathematics Computational Mathematics Range (mathematics) 10123 Institute of Mathematics Modeling and Simulation Element (category theory) 2605 Computational Mathematics Analysis 2611 Modeling and Simulation |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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