The finite volume implementation of the partial asymptotic domain decomposition

Abstract:

The method of asymptotic partial domain decomposition (MAPDD) 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. The article is devoted to the finite volume implementation of the MAPDD. We consider a model conductivity problem in a thin domain (its thickness is a small parameter). Applying the MAPDD, we implement then the finite volume method and obtain an error estimate, expressed in terms of the small parameter and the step of the mesh.

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

Document Type: Research article

DOI: 10.1080/00036810802282533

Affiliations: 1: LaMUSE EA 3989, University Jean Monnet, Saint Etienne, France