Mixed finite element discretization of a model for organic pollution in waters Part I. The problem and its discretization

Faker Ben Belgacem (1) , Christine Bernardi (2) , Frédéric Hecht (2) , Stéphanie Salmon (3)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne
2 LJLL - Laboratoire Jacques-Louis Lions
3 LMR - Laboratoire de Mathématiques de Reims

We consider a mixed reaction diffusion system describing the organic pollution in stream-waters. It may be viewed as the static version of Streeter-Phelps equations relating the Biochemical Oxygen Demand and Dissolved Oxygen to which dispersion terms are added. In this work, we propose a mixed variational formulation and prove its well-posedness. Next, we develop two finite element discretizations of this problem and establish optimal a priori error estimates for the second discrete problem.

Mots clés: Variational formulation; non-symmetric mixed problem; mixed finite elements; gen- eralized saddle point theory; organic pollution.; organic pollution

Domaines: Analyse numérique [math.NA]

Faker Ben Belgacem, Christine Bernardi, Frédéric Hecht, Stéphanie Salmon. Mixed finite element discretization of a model for organic pollution in waters Part I. The problem and its discretization. 2013. ⟨hal-00781238⟩