Derivation and Analysis of Piecewise Constant Conservative Approximation for Anisotropic Diffusion Problems

A. Agouzal (1, 2) , Naïma Debit (1)

1 ICJ - Institut Camille Jordan
2 MMCS - Modélisation mathématique, calcul scientifique

A variational approach to derive a piecewise constant conservative approximation of anisotropic diffusion equations is presented. A priori error estimates are derived assuming usual mesh regularity constraints and a posteriori error indicator is proposed and analyzed for the model problem.

Mots clés: Finite elements; conservative approximation; a posteriori error estimate

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

A. Agouzal, Naïma Debit. Derivation and Analysis of Piecewise Constant Conservative Approximation for Anisotropic Diffusion Problems. 2009. ⟨hal-00360259v2⟩