A unified treatment of boundary conditions in least-square based finite-volume methods
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. (c) 2005 Elsevier Ltd. All rights reserved.
least-squares reconstruction robin boundary conditions finite volume unstructured mesh neumann boundary conditions