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

AMS Subject Classifications: :

• 35B27
• 35Q53
• 35C20
• 35J25
• 65N12
• 65N15
• 76M12

Acknowledgements

This work is supported by the Region Rhône-Alpes grant ‘Modélisation multi-échelle des nanostructures’ 04 022487 01, by the multi-disciplinary grant ALLIANA and by the French-Russian and French-Romanian PICS CNRS grants.