A posteriori error estimation for the discrete duality finite volume discretization of the Laplace equation

Pascal Omnes (1, 2) , Yohan Penel (1, 2) , Yann Rosenbaum (1, 2)

1 SFME - Service Fluide numériques, Modélisation et Etudes
2 LAGA - Laboratoire Analyse, Géométrie et Applications

An efficient and fully computable a posteriori error bound is derived for the discrete duality finite volume discretization of the Laplace equation on very general twodimensional meshes. The main ingredients are the equivalence of this method with a finite element like scheme and tools from the finite element framework. Numerical tests are performed with a stiff solution on highly nonconforming locally refined meshes and with a singular solution on triangular meshes.

Keywords: a posteriori error estimation; finite volume; discrete duality; nonconforming meshes

Domains: Mathematics [math]; Numerical Analysis [math.NA]

Pascal Omnes, Yohan Penel, Yann Rosenbaum. A posteriori error estimation for the discrete duality finite volume discretization of the Laplace equation. SIAM Journal on Numerical Analysis, 2009, 47 (4), pp.2782--2807. ⟨10.1137/080735047⟩. ⟨cea-00320486v2⟩