A family of mixed finite elements for the elasticity problem
Numerische Mathematik
A local post-processing technique for improving the accuracy in mixed finite-element approximations
SIAM Journal on Numerical Analysis
Spectral methods on triangles and other domains
Journal of Scientific Computing
Hierarchical hp finite elements in hybrid domains
Finite Elements in Analysis and Design - Special issue: Robert J. Melosh medal competition
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Velocity-Correction Projection Methods for Incompressible Flows
SIAM Journal on Numerical Analysis
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
SIAM Journal on Numerical Analysis
Analysis of a Multiscale Discontinuous Galerkin Method for Convection-Diffusion Problems
SIAM Journal on Numerical Analysis
Locally Conservative Fluxes for the Continuous Galerkin Method
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems
SIAM Journal on Numerical Analysis
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
SIAM Journal on Scientific Computing
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 0.01 |
Hybridization through the border of the elements (hybrid unknowns) combined with a Schur complement procedure (often called static condensation in the context of continuous Galerkin linear elasticity computations) has in various forms been advocated in the mathematical and engineering literature as a means of accomplishing domain decomposition, of obtaining increased accuracy and convergence results, and of algorithm optimization. Recent work on the hybridization of mixed methods, and in particular of the discontinuous Galerkin (DG) method, holds the promise of capitalizing on the three aforementioned properties; in particular, of generating a numerical scheme that is discontinuous in both the primary and flux variables, is locally conservative, and is computationally competitive with traditional continuous Galerkin (CG) approaches. In this paper we present both implementation and optimization strategies for the Hybridizable Discontinuous Galerkin (HDG) method applied to two dimensional elliptic operators. We implement our HDG approach within a spectral/hp element framework so that comparisons can be done between HDG and the traditional CG approach.We demonstrate that the HDG approach generates a global trace space system for the unknown that although larger in rank than the traditional static condensation system in CG, has significantly smaller bandwidth at moderate polynomial orders. We show that if one ignores set-up costs, above approximately fourth-degree polynomial expansions on triangles and quadrilaterals the HDG method can be made to be as efficient as the CG approach, making it competitive for time-dependent problems even before taking into consideration other properties of DG schemes such as their superconvergence properties and their ability to handle hp-adaptivity.