Related papers: A hybridizable discontinuous Galerkin method for t…
We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations. The divergence-free condition is enforced on the electric field, then a Lagrange multiplier is introduced, and the problem…
In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous…
We propose to use a hybridizable discontinuous Galerkin (HDG) method combined with the continuous Galerkin (CG) method to approximate Maxwell's equations. We make two contributions in this paper. First, even though there are many papers…
This paper analyzes the error estimates of the hybridizable discontinuous Galerkin (HDG) method for the Helmholtz equation with high wave number in two and three dimensions. The approximation piecewise polynomial spaces we deal with are of…
Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell's equations in the time domain are presented. The first method is based on an electromagnetic diffusion equation, while the second is based on Faraday's and…
We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduction of an HDG flux of the dual saddle-point form of the MHD…
The CHDG method is a hybridizable discontinuous Galerkin (HDG) finite element method suitable for the iterative solution of time-harmonic wave propagation problems. Hybrid unknowns corresponding to transmission variables are introduced at…
We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…
We derive and analyze a hybridizable discontinuous Galerkin (HDG) method for approximating weak solutions to the equations of time-harmonic linear elasticity on a bounded Lipschitz domain in three dimensions. The real symmetry of the stress…
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…
This paper develops and analyzes an interior penalty discontinuous Galerkin (IPDG) method using piecewise linear polynomials for the indefinite time harmonic Maxwell equations with the impedance boundary condition in the three dimensional…
We propose a hydridizable discontinuous Galerkin (HDG) method for solving the Cahn-Hilliard equation. The temporal discretization can be based on either the backward Euler method or the convex-splitting method. We show that the fully…
We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…
In this paper, we present a flux-based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems and propose a new method derived by letting a stabilization parameter tend to infinity. Assuming…
This paper develops an hybridizable discontinuous Galerkin (HDG) finite element method of arbitrary order for the steady thermally coupled incompressible Magnetohydrodynamics (MHD) flow. The HDG scheme uses piecewise polynomials of degrees…
In this paper we present new stability and optimal error analyses of hybridized discontinuous Galerkin (HDG) methods which do not require elliptic regularity assumptions. To obtain error estimates without elliptic regularity assumptions, we…
We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. These problems can involve atypical variational formulations,…
A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed for solving time-harmonic scalar wave propagation problems. This method relies on a standard discontinuous Galerkin scheme with upwind numerical fluxes and…
We develop and analyze the first hybridizable discontinuous Galerkin (HDG) method for solving fifth-order Korteweg-de Vries (KdV) type equations. We show that the semi-discrete scheme is stable with proper choices of the stabilization…
We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and…