A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation

By Carl Ollivier-Gooch, Michael Van Altena. 2002

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Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems (2007, methodology): “The design of higher order finite volume methods usually requires a reconstruction (or recovery) procedure starting from cell averages and yielding higher order polynomials, see [1,4,25,37,30,41,43].”
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems (2007, methodology): “For robustness purposes, more elements than the minimum needed for reconstruction of a polynomial of degree M are used, see also [4,30,27].”
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (2008, methodology): “Since (11) becomes overdetermined with the choice ne > LM/LN we use a constrained least-squares technique in order to solve (11) respecting conservation of all degrees of freedom up to degree N in the first element T (m) of the stencil, i.e. we require ŵ (m) pl = û (m) pl , for 1 ≤ l ≤ LN .”