Discontinuous Galerkin approximations for elliptic problems

By Franco Brezzi, Gianmarco Manzini, Donatella Marini, Paola Pietra, Alessandro Russo. 2000

418 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1371d0fa7a07d3c2dd2c3865bb8eb09a51ac1727

How researchers see this paper

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

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: Motivation, formulation, and numerical examples (2008, methodology): “As shown in [11,24] and discussed later, a sense of the magnitude of the discontinuities across element boundaries can be obtained with any norm for ||R([[φh − v̂(φh)]])||.”
A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications (2006, methodology): “At this point, an assumed form of the deformation gradients is adopted extending to finite deformations of solids the assumed scalar gradients in Brezzi et al [9], see also [11]: Fh = ∇0ϕh + Rϕ̄h (JϕhK) (25) where the tensorial operator Rϕ̄h : L 2 (∂IB0h) → Skh is defined as: ∫ B0h Rϕ̄h (JvK) : τdV0”
Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case (2007, methodology): “From the definition (3) of re, and after using the trace inequality (12) as in [11], we have C1h −1 e ‖φ‖(2)0,e ≤ ‖re(φ)‖(2)0,Ω ≤ C2h e ‖φ‖(2)0,e ∀φ ∈ [ M h(e) ]d , (14) with constants C1 and C2 only depending on the minimum angle of the partition and the polynomial degree h.”
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems (2001, methodology): “[29], and the variations of the method of Baumann and Oden introduced and studied by Rivière et al.”
Discontinuous Galerkin methods for non‐linear elasticity (2006, methodology): “It was shown in Reference [13], closely following the developments in Reference [15], that the choice of Bassi and Rebay numerical fluxes for the linear elastic case results in a discrete bilinear form that may not be coercive, i.”
A discontinuous‐Galerkin‐based immersed boundary method (2008, background): “, in [42, 11]) consists of adding, to the left-hand side of (37), the term”
On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations (2012, background): “[4], we include it hereafter for the sake of completeness.”
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations (2005, background): “For p P 1, optimal accuracy can be proven using this stability result [18,17].”
A Reconstruction Approach to High -Order Schemes Including Discontinuous Galerkin for Diffusion (2009, background): “This modification, often called BR2, was analyzed in (Brezzi et al. 2000).”
Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations ofElliptic Problems (2007, neutral): “Finally, we define the local lifting operators (see [4,14]) re : [L(2)(e)] −→ Σh and le : L(2)(e) −→ Σh by ∫”
Discontinuous Galerkin solution of the Reynolds-averaged Navier–Stokes and k–ω turbulence model equations (2005, methodology): “e notation J and J has been preferred to that used in [2,3,11] since it reflects the vector nature of the jump tor and because its usage is analogous to that of the well known $ and $ operators.”