Theoretical and numerical investigation of the finite cell method

Monique Dauge (1) , Alexander Düster (2) , Ernst Rank (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 TUHH - Technische Universität Hamburg-Harburg
3 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich

We present a detailed analysis of the convergence properties of the finite cell method which is a fictitious domain approach based on high order finite elements. It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lame problems in one, two as well as three dimensions. Several numerical examples in one and two dimensions including a well-known benchmark problem from linear elasticity confirm the results of the mathematical analysis of the finite cell method.

Mots clés: high order methods; fictitious domain methods; finite cell method; p-FEM; exponential convergence

Domaines: Analyse numérique [math.NA]; Analyse numérique [cs.NA]; Modélisation et simulation; Mécanique [physics.med-ph]

Monique Dauge, Alexander Düster, Ernst Rank. Theoretical and numerical investigation of the finite cell method. Journal of Scientific Computing, 2015, 65 (3), pp.1039-1064. ⟨10.1007/s10915-015-9997-3⟩. ⟨hal-00850602v3⟩