Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

By Bernardo Cockburn, Jay Gopalakrishnan, Raytcho D. Lazarov. SIAM Journal on Numerical Analysis, 2009

1,272 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3768f4aa6673e6b767016195ff250bf660f1ccc7

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 Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A hybrid mixed discontinuous Galerkin finite-element method for convection–diffusion problems (2010, background): “In numerical tests, we illustrated the efficiency of our approach and compare to results obtained with other methods for convection diffusion problems.”
Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems (2013, methodology): “This procedure ensures a well posed problem and the superconvergent properties of the method, see [38].”
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods (2016, methodology): “As defined in [8], the LDG-H methods are the HDG methods obtained when the local discontinuous Galerkin (LDG) method is used to define the local problems.”
Analysis of an HDG method for linear elasticity (2015, methodology): “A new brand of DG methods, the HDG methods, appeared in 2009 [16] in the framework of second-order elliptic problems.”
A hybridizable discontinuous Galerkin method for linear elasticity (2009, methodology): “Part of this vigorous development was the recent introduction of the HDG methods in [22] for second-order scalar elliptic problems.”
Multigrid for an HDG method (2013, methodology): “It is proved in (Cockburn et al., 2009b) that the system (2.5) is uniquely solvable if τK is positive on at least one face of K for every element K.”
Efficiency of high‐order elements for continuous and discontinuous Galerkin methods (2013, background): “Recall, see [13, 14], that HDG presents, for elliptic operators, a super-convergent property that produces a solution with an extra order of approximation after an inexpensive element-by-element post-process.”
A weak Galerkin finite element method for second-order elliptic problems (2011, methodology): “The standard mixed finite elements ([20, 2, 4, 8, 9, 11, 10, 24]) and various discontinuous Galerkin methods based on both variables ([12, 14, 16, 19]) are representatives of the second category.”
An Overview of the Discontinuous Petrov Galerkin Method (2014, methodology): “The DPG method is definitely more expensive than standard, conforming finite elements or hybridizible DG elements [19].”
Forty Years of the Crouzeix‐Raviart element (2015, background): “A general discussion on hybridization can be found in [59].”
hp analysis of a hybrid DG method for Stokes flow (2013, background): “This result holds on irregular and hybrid meshes in two and three spatial dimensions, and its proof is based on a new stability estimate for the L2 projection on simplex elements.”
Finite Element Methods for Maxwell's Equations (2019, methodology): “Hybridizable discontinuous Galerkin (HDG) methods [24] were recently introduced with the aim of reducing the dimension of the discrete global linear system that needs to be solved and deliver superconvergent recovery of variables of interest.”
A class of discontinuous Petrov–Galerkin methods. II. Optimal test functions (2011, positive): “While earlier research concentrated on tailoring numerical fluxes for upwinding, maintaining high approximation order, and addition of stabilization terms [4, 15, 22], there is a resurgence of interest [20, 31] focusing on adapting the recent hybridized (HDG) framework [14] to convective problems.”