document: A popular choice is to couple a set of quadrature points with an equal number of nodal Lagrange polynomials defined at the same points, leading to a collocation method. There are many examples of this throughout the literature, both in terms of the more traditionally utilised continuous Galerkin (CG) and discontinuous Galerkin (DG) formulations, as well as newer extensions such as the flux reconstruction (FR) technique as presented by Huynh [23]. In collocation methods, while most linear operators can be exactly integrated in this setting depending on the choice of quadrature, integrals of nonlinear terms typically incur numerical error. However, the computational efficiencies that can be attained through the use of a collocation formulation, especially given the presence of a diagonal mass matrix, often outweigh the numerical error that is incurred.
extractive_keyphrases: cg collocation method collocation methods couple a set of quadrature points with an equal number of nodal lagrange polynomials dg discontinuous galerkin flux reconstruction fr galerkin linear operators newer extensions
abstractive_keyphrases: collocation formulation, especially given the presence of a diagonal mass matrix