Before revision:  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:  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, highlighting the design choices afforded for methods within the proposed framework and corroborating the theoretical results .