Error estimate in a finite volume approximation of the partial asymptotic domain decomposition.

Grigory Panasenko (1) , Marie-Claude Viallon (2)

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

The method of asymptotic partial domain decomposition (MAPDD) has been proposed for partial differential equations set in rod structures, depending on a small parameter. It reduces the dimension of the problem (or simplifies it in another way) in the main part of the domain keeping the initial formulation in the remaining part and prescribing the asymptotically precise conditions on the interface. This paper is devoted to the finite volume implementation of the MAPDD. We consider a model problem in a thin domain (its thickness is a small parameter). We obtain an error estimate, expressed in terms of the small parameter and the step of the mesh.

Mots clés: energy estimates; homogenization; asymptotic expansion; finite volume scheme; elliptic problem

Domaines: Equations aux dérivées partielles [math.AP]

Grigory Panasenko, Marie-Claude Viallon. Error estimate in a finite volume approximation of the partial asymptotic domain decomposition.. Mathematical Methods in the Applied Sciences, 2013, 36 (14), pp.1892-1917. ⟨10.1002/mma.2735⟩. ⟨hal-00916745⟩