In this paper we attack the problem of devising a finite volume method for computational fluid dynamics and related phenomena which can deal with complex geometries while attaining high-orders of accuracy and spectral convergence at a reasonable computational cost. As a first step towards this end, we propose a control volume finite element method for the solution of the advection–diffusion equation. The numerical method and its implementation are carefully tested in the paper where h- and p-convergence are checked by comparing numerical results against analytical solutions in several relevant test-cases. The numerical efficiency of a selected set of operations implemented is estimated by operation counts, ill conditioning of coefficient matrices is avoided by using an appropriate distribution of interpolation points and control-volume edges.
Development of a mixed control volume – Finite element method for the advection–diffusion equation with spectral convergence / M., Piller; Stalio, Enrico. - In: COMPUTERS & FLUIDS. - ISSN 0045-7930. - STAMPA. - 40:(2011), pp. 269-279. [10.1016/j.compfluid.2010.09.026]