Mathematical Aspects of Discontinuous Galerkin Methods

By Daniele A. Di Pietro, Alexandre Ern. 2011

1,241 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2d1ccfdc0ccc8884b68cb44a1efc4102cf47bf6b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

Citations in the corpus

A discontinuous skeletal method for the viscosity-dependent Stokes problem (2015, neutral): “Then, we get Using the H 1 -stability of π kT (cf. [14, Lemma 1.58] and [12, Corollary 3.7]), it is readily inferred that T 1 À } ∇ v } T .”
Transient field distribution in gas-solid insulation systems under DC voltages (2014, methodology): “The equation system is transformed into the weak formulation and terms for “interior penalty”- and “upwind”-stabilization are added [33, 34].”
On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations (2012, methodology): “We hence adopt a different point of view, proposed by Tesini [19], where discrete polynomial spaces defined in physical coordinates are proposed as the key ingredient to handle general meshes; see also Di Pietro and Ern [5,6].”
hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes (2016, neutral): “2 TITLE WILL BE SET BY THE PUBLISHER first appeared around the same time [12, 13]; for reviews of some of the main developments in the subject, we refer to the monographs [27,28] and the articles [8, 24].”
Virtual Element Methods for general second order elliptic problems on polygonal meshes (2014, neutral): “We recall for instance [4], [5], [6], [7], [8], [20], [21], [31], [34], [38], [41], [42], [43], [44] [47], [48], [51], [52], [58], [57], [60], [61], [62], [63], [65], [66], [67], [70].”
A Hybrid High-Order method for the incompressible Navier-Stokes equations based on Temam's device (2018, neutral): “In Section 2, we recall the de nition of admissible mesh sequences in the spirit of [9] as well as some useful results, and we de ne the interpolation operator.”
Dissipative Gradient Nonlinearities Prevent δ$\delta$ ‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models (2024, positive): “In particular, regarding the spatial approximation, we use an upwind discontinuous Galerkin (DG) method [10] with piecewise constant polynomials defined on a triangular/tetrahedral mesh of the ( 2 -dimensional/ 3 -dimensional) domain Ω with size h .”
On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime (2014, background): “From the continuity of the normal components of vh, one concludes that RTh ⊂ H(div ; Ω) holds [16].”
Morley Finite Element Method for the Eigenvalues of the Biharmonic Operator (2014, background): “…T satisﬁes Dϕ 3 | T = (dist( z 3 , F )) − 1 ν T as well as Deﬁne the operator A : V ℓ → V which acts as e An immediate consequence of this choice reads as e An integration by parts shows the integral mean property of the Hessian T and the trace inequality [11, 22] prove, for any T ∈ T ℓ , that .”