Discrete Poincaré inequalities for arbitrary meshes in the discrete duality finite volume context
Abstract
We establish discrete Poincaré type inequalities on a twodimensional polygonal domain covered by arbitrary, possibly nonconforming meshes. On such meshes, discrete scalar fields are defined by their values both at the cell centers and vertices, while discrete gradients are associated with the edges of the mesh, like in the discrete duality finite volume scheme. We prove that the constants that appear in these inequalities depend only on the domain and on the angles in the diagonals of the diamond cells constructed by joining the two vertices of each mesh edge and the centers of the cells that share that edge.
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