A Fast High Order Arbitrary Lagrangian Eulerian Transformation

Gonçalo Pena (1) , Vincent Chabannes (2) , Christophe Prud'Homme (3, 2)

1 CMUC - Center for Mathematics [Coimbra]
2 EDP - Equations aux Dérivées Partielles
3 IRMA - Institut de Recherche Mathématique Avancée

In this article we propose a high order Arbitrary Lagrangian Eulerian framework with optimal accuracy and efficiency. The construction is done in two steps, the first one follows the standard construction while the second step builds a high order correction with the solution of a local differential operator, enabling any types of displacements as well as domain shapes. Finally we verify on a 3D example that we recover the expected accuracy for first to fourth order geometries.

Mots clés: high order methods; Arbitrary Lagrangian Eulerian

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Gonçalo Pena, Vincent Chabannes, Christophe Prud'Homme. A Fast High Order Arbitrary Lagrangian Eulerian Transformation. 2011. ⟨hal-00657099⟩