An Overview of the Discontinuous Petrov Galerkin Method

Chapter 6: Overview of Variational Formulations for Linear Elliptic PDEs

“…In [44] (and subsequent papers) the polynomial part of the space was dropped, and then since there was no longer any "enrichment," the method was called a DG method (and abbreviated to DGM); see [44, of 1 , the method defines so-called optimal test spaces 2 N of 2 ; these optimal test spaces are such that, when the sesquilinear form satisfies the inf-sup condition (6.40), the discrete infsup condition (6.46) is automatically satisfied; see, e.g., [59,Proposition 5]. These optimal test spaces admit functions with no continuity constraints across element interfaces, hence the "discontinuous" in "DPG" [59,Definition 16], [29,Section 3]. In practice, the optimal test spaces are not computed exactly (since this would require solving BVPs on each K ∈ ) but instead are approximated [59,Section 3].…”

Multiscale Petrov‐Galerkin FEM for Acoustic Scattering

“…For the case of variable material coefficients, see [1]. We remark that the proposed Petrov-Galerkin shares some properties with the discontinuous Petrov-Galerkin method [2,3], and it appears worth investigating these connections in future work.…”

An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms

“…In this context, the use of different test norms to stabilize convection-diffusion problems was further investigated in [14]. Interestingly, the idea of residual minimization in nonstandard dual norms is also at the heart of the recent Discontinuous Petrov-Galerkin (DPG) methods (see, e.g., [40,20,15], and [19] for a general overview). Alternatively, several strategies based on fluctuation stabilization exist.…”