A unified treatment of boundary conditions in least-square based finite-volume methods

Authors:
E. Bertolazzi;G. Manzini
Affiliations:
Dip. Ingegneria Meccanica e Strutturale Università di Trento via Mesiano 77, Trento, Italy;Istituto di Matematica Applicata e Tecnologie Informatiche I.M.A.T.I. - C.N.R., Via Ferrata, 1, Pavia, Italy
Venue:
Computers & Mathematics with Applications
Year:
2005

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Abstract

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.