Constraint oriented spectral element method

Etienne Ahusborde (1) , M. Azaïez (2) , R. Gruber (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 TREFLE - Transferts, écoulements, fluides, énergétique
3 EPFL - Ecole Polytechnique Fédérale de Lausanne

An original polynomial approximation to solve partial differential equations is presented. This spectral element version takes into account the underlying nature of the corresponding physical problem. For different types of operators, this approach allows to all terms in a variational form to be represented by the same functional dependence and by the same regularity, thus eliminating regularity constraints imposed by standard numerical methods. This method satisfies automatically different type of constraints, such as occur for the grad(div) and curl(curl) operators, and this for any geometry. It can be applied to a wide range of physical problems [Physical Review E, 75(5), 056704 (2007)], including fluid flows, electromagnetism, material sciences, ideal linear magnetohydrodynamic stability analysis, and Alfvèn wave heating of fusion plasmas [Communications in Computational Physics, 5(2-4), 413-425 (2009)]. © 2011 Springer.

Domaines: Analyse numérique [math.NA]

Etienne Ahusborde, M. Azaïez, R. Gruber. Constraint oriented spectral element method. Lecture Notes in Computational Science and Engineering, 2011, 76 LNCSE, pp.93-100. ⟨hal-00861285⟩