Principles of a network element method

Julien Coatléven (1)

1 IFPEN - IFP Energies nouvelles

We introduce a new variational numerical method which does not require any background mesh to compute the scheme coefficients. Replacing the mesh by a point cloud endowed with connectivity, which we call a discretization network, and following the virtual element framework we derive a consistent, coercive and stable numerical scheme. We illustrate the good behavior of the method on several numerical examples.

Mots clés: Poisson equation; meshless methods; variational methods; virtual element method; mimetic finite differences; 65N12; 65N15; 65N30 Evolution problems

Domaines: Mathématiques [math]

Julien Coatléven. Principles of a network element method. Journal of Computational Physics, 2021, 433, pp.110197. ⟨10.1016/j.jcp.2021.110197⟩. ⟨hal-03245165⟩