The Continuous Galerkin Method Is Locally Conservative

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Finite Volume Methods (2019, methodology): “1 The piecewise linear finite element method viewed as a finite volume method Links between the finite volume method and the finite element method have already been explored [88, 90, 137].”
Weak imposition of Dirichlet boundary conditions in fluid mechanics (2007, background): “[33]): Find u ∈ H(1) g (Ω), q ∈ H (Γ) such that ∀w ∈ H(1)(Ω), (−∇w,au − k∇u)Ω− < w, q >Γ −(w, f)Ω = 0 (16) where < ·, · >Γ denotes a duality pairing between H(Γ) and H(Γ) .”
Adaptive variational multiscale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems (2007, background): “See [11] for further discussion on variational approximation of the flux.”
Mixed finite elements for solving 2‐D diffusion‐type equations (2010, methodology): “Note, however, that postprocessing techniques can be employed to enhance the velocity field approximation [Cordes and Kinzelbach, 1992; Loula et al., 1995; Hughes et al., 2000; Correa and Loula, 2007].”
Locally conservative, stabilized finite element methods for variably saturated flow (2008, methodology): “The general conservation properties of CG methods for advection-diffusion-reaction equations and incompressible Navier-Stokes were investigated in [19, 22].”