Before revision:  Situating such components common to DG and FR methods within the context of the summation-by-parts property, a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
After revision:  Situating such components common to DG and FR schemes. Specifically, the analysis enables the extension of the equivalence between the strong and weak forms of the discontinuous Galerkin collocation spectral-element method demonstrated by Kopriva and Gassner (J Sci Comput 44:136-155, 2010) to more general nodal and modal DG formulations, as well as to the Vincent-Castonguay-Jameson-Huynh (VCJH) family of FR methods. Moreover, new algebraic proofs of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations, corroborating the theoretical results .