Journal of Computational Physics
A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems
Journal of Scientific Computing
Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains
Journal of Scientific Computing
Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams
Journal of Scientific Computing
Journal of Computational Physics
A Hybrid Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
Journal of Computational Physics
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations
Journal of Computational Physics
Error Analysis for a Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation
Journal of Scientific Computing
A Mixed Method for the Biharmonic Problem Based On a System of First-Order Equations
SIAM Journal on Numerical Analysis
Analysis of the DPG Method for the Poisson Equation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Recovery of normal derivatives from the piecewise L2 projection
Journal of Computational Physics
Journal of Computational Physics
To CG or to HDG: A Comparative Study
Journal of Scientific Computing
A Posteriori Error Estimates for HDG Methods
Journal of Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
Coupling at a Distance HDG and BEM
SIAM Journal on Scientific Computing
Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains
SIAM Journal on Scientific Computing
A weak Galerkin finite element method for second-order elliptic problems
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation
Journal of Computational Physics
Journal of Scientific Computing
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We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continuous Galerkin, nonconforming, and a new, wide class of hybridizable discontinuous Galerkin methods. The distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements. Since the associated matrix is sparse, symmetric, and positive definite, these methods can be efficiently implemented. Moreover, the framework allows, in a single implementation, the use of different methods in different elements or subdomains of the computational domain, which are then automatically coupled. Finally, the framework brings about a new point of view, thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques, as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom.