A projection-based error analysis of HDG methods

By Fatih Celiker, Bernardo Cockburn, Ke Shi. Mathematics of Computation, 2010

295 citations recorded by the source corpus.

We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG method applied to a model second-order elliptic problem.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/feed5ed4b13649ecb2ba094e56d6e09dd33732e3

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In Computational Mechanics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Analysis of an HDG method for linear elasticity (2015, background): “The theoretical understanding of this loss of superconvergence for some types of meshes, a property typically enjoyed by the HDG methods for quite general meshes, the diffusion problem [17, 18, 38], the gradient formulation of the Stokes problem [28], and the weak symmetry formulation for linear ela”
A high‐order hybridizable discontinuous Galerkin method for elliptic interface problems (2013, unknown): “We recall from [8–10] that the HDG method for standard elliptic problems without interface conditions is deﬁned as follows: ﬁnd .”
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods (2016, methodology): “Note that the operator p k`1 h is a small variation of the post-processings used in [10,11], where a proper subspace ofW pT q is used instead ofW pT q.”
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses (2013, methodology): “Many mixed methods have been proposed which use the above system (Arnold et al. 1984, 2007; Stenberg 1988; Boffi et al. 2009; Qiu & Demkowicz 2009, 2011; Cockburn et al. 2010; Gopalakrishnan & Guzmán; Guzmán 2010).”