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Theoretical analysis of the upwind finite volume scheme on the counter-example of Peterson
2010
Mathematical Modelling and Numerical Analysis
When applied to the linear advection problem in dimension two, the upwind finite volume method is a non consistent scheme in the finite differences sense but a convergent scheme. According to our previous paper [Bouche et al., SIAM J. Numer. Anal. 43 (2005) 578-603], a sufficient condition in order to complete the mathematical analysis of the finite volume scheme consists in obtaining an estimation of order p, less or equal to one, of a quantity that depends only on the mesh and on the
doi:10.1051/m2an/2010026
fatcat:mpb26escyzewjkeh7vpzbqjtyq