A mesh adaptivity scheme on the Landau–de Gennes functional minimization case in 3D, and its driving efficiency

Iztok Bajc (1) , Frédéric Hecht (2, 3) , Slobodan Žumer (4, 1)

1 Univerza v Ljubljani
2 LJLL - Laboratoire Jacques-Louis Lions
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
4 IJS - Jozef Stefan Institute [Ljubljana]

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics derived from the Hessian of a solution. The study is made on the case of a nonlinear finite element minimization scheme for the Landau–de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in.

Mots clés: Finite elements; Metrics; 3D mesh adaptivity; Nematic liquid crystals; PDE; Nonlinear analysis

Domaines: Physique [physics]

Iztok Bajc, Frédéric Hecht, Slobodan Žumer. A mesh adaptivity scheme on the Landau–de Gennes functional minimization case in 3D, and its driving efficiency. Journal of Computational Physics, 2016, 321, pp.981-996. ⟨10.1016/j.jcp.2016.02.072⟩. ⟨hal-01360423⟩