Finite volume method for an elliptic problem in 3d

Abstract

This thesis is devoted to the spectral analysis of a three-dimensional elliptic problem using the finite volume method. After presenting the functional framework, Sobolev spaces, and the main results of spectral theory, a variational formulation of the problem is established. A finite volume discretization on a structured three-dimensional mesh is then developed. The proposed scheme has been validated through numerical tests. The obtained results demonstrate the accuracy of the numerical scheme.