A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
An Analysis of New Mixed Finite Elements for the Approximation of Wave Propagation Problems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Optimal Discontinuous Galerkin Methods for Wave Propagation
SIAM Journal on Numerical Analysis
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems
Journal of Scientific Computing
Journal of Computational Physics
The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
SIAM Journal on Scientific Computing
Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
SIAM Journal on Numerical Analysis
A Comparison of HDG Methods for Stokes Flow
Journal of Scientific Computing
Journal of Computational Physics
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
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We present a class of hybridizable discontinuous Galerkin (HDG) methods for the numerical simulation of wave phenomena in acoustics and elastodynamics. The methods are fully implicit and high-order accurate in both space and time, yet computationally attractive owing to their following distinctive features. First, they reduce the globally coupled unknowns to the approximate trace of the velocity, which is defined on the element faces and single-valued, thereby leading to a significant saving in the computational cost. In addition, all the approximate variables (including the approximate velocity and gradient) converge with the optimal order of k+1 in the L^2-norm, when polynomials of degree k=0 are used to represent the numerical solution and when the time-stepping method is accurate with order k+1. When the time-stepping method is of order k+2, superconvergence properties allows us, by means of local postprocessing, to obtain better, yet inexpensive approximations of the displacement and velocity at any time levels for which an enhanced accuracy is required. In particular, the new approximations converge with order k+2 in the L^2-norm when k=1 for both acoustics and elastodynamics. Extensive numerical results are provided to illustrate these distinctive features.