Istituto di Matematica Applicata e Tecnologie Informatiche     
Bertolazzi E., Manzini G. A unified treament of boundary conditions in least square-based Finite Volume methods. Preprint ercim.cnr.ian//2002-1311, 2002.
We propose a unified treatment of internal and boundary vertex Least Squares reconstructions in second-order accurate cell-centered finite volume discretisation of 2-D steady diffusion problems. Dirichlet, Neumann and Robin boundary conditions are taken into account in the same formulation by introducing suitable constraints in the Least Squares minimization process. The method is discussed in its theoretical framework and a representative numerical experiment illustrates its capability in providing the second order of accuracy.
Subject Finite Volume, Unstructured mesh, Neumann Boundary Conditions, Robin Boundary Conditions, Least Squares reconstruction.

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