Superconvergent HDG methods for linear elasticity with weakly symmetric stresses

By Bernardo Cockburn, Ke Shi. 2013

66 citations recorded by the source corpus.

We provide a systematic way of devising superconvergent mixed and hybridizable discontinuous Galerkin (HDG) methods for linear elasticity based on weak stress symmetry formulations. We show that, by suitably modifying the spaces defining superconvergent mixed and HDG methods for diffusion obtained in Cockburn et al. (Conditions for superconvergence of HDG methods for second-order elliptic problems, Math. Comp., 81, 1327–1353.), we obtain optimally convergent approximations for all unknowns, as well as a superconvergent approximation of the displacement. We use a projection-based a priori error analysis to achieve this goal.

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

View Paper: https://www.semanticscholar.org/paper/964862cedafe31528b81ac3f5c810066788703c4

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

1. Henry K. Stolarski
2. Guosheng Fu
3. Bernardo Cockburn
4. Chi-Wang Shu
5. Dominik Schötzau
6. Antonio Huerta
7. Guido Kanschat
8. Yan Xu

In Electrical and Electronic Engineering

1. Henry K. Stolarski
2. Guosheng Fu
3. Bernardo Cockburn
4. Alexandre Ern
5. Ke Shi
6. Xiu Ye
7. Junping Wang
8. Antonio Huerta

In Mechanics of Materials

1. Henry K. Stolarski
2. Guosheng Fu
3. Bernardo Cockburn

Citations in the corpus

• Analysis of an HDG method for linear elasticity (2015, methodology): “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”