A discrete duality finite volume method for elliptic problems with corner singularities

We focus on the Discrete Duality Finite Volume (DDFV) method whose particularity is to allow the use of unstructured or nonconforming meshes. We deal with the Laplacian problem on nonconvex domains. We show how appropriate refinement conditions on the diamond mesh lead to an optimal order of convergence as for smooth solutions. These theoretical results are illustrated by some numerical applications.