Related papers: A hybridizable discontinuous Galerkin method with …
In this work we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential weights when computing the $L^2$ product in each cell of the discretization, we are able to…
In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, and have been successfully applied to a wide range of…
Weight-adjusted inner products are easily invertible approximations to weighted $L^2$ inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time-domain method for wave propagation…
In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad-Shafranov equation, the solution of which determines the poloidal…
This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, which makes adaptivity essential in improving the simulation…
Spacetime discontinuous Galerkin (SDG) finite element methods are used to solve such PDEs involving space and time variables arising from wave propagation phenomena in important applications in science and engineering. To support an…
We propose and analyse a fully-discrete discontinuous Galerkin time-stepping method for parabolic Hamilton--Jacobi--Bellman equations with Cordes coefficients. The method is consistent and unconditionally stable on rather general…
The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from…
We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence rate for…
In the spirit of making high-order discontinuous Galerkin (DG) methods more competitive, researchers have developed the hybridized DG methods, a class of discontinuous Galerkin methods that generalizes the Hybridizable DG (HDG), the…
The quad-curl problem arises in magnetohydrodynamics, inverse electromagnetic scattering and transform eigenvalue problems. In this paper we investigate a hybridizable discontinuous Galerkin method to solve the quad-curl problem based on a…
We have extended Cosmos++, a multi-dimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and…
In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the…
This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schr\"odinger equation with the wave operator. The focus of the study is on the energy-conserving or energy-dissipating behavior of the method with…
We consider the damped time-harmonic Galbrun's equation, which is used to model stellar oscillations. We introduce a discontinuous Galerkin finite element method (DGFEM) with $H(\operatorname{div})$-elements, which is nonconform with…
Simulation of wave propagation through complex media relies on proper understanding of the properties of numerical methods when the wavenumber is real and complex. Numerical methods of the Hybrid Discontinuous Galerkin (HDG) type are…
Wormhole propagation plays a very important role in the product enhancement of oil and gas reservoir. A new combined hybrid mixed finite element method is proposed to solve incompressible wormhole propagation problem with discontinuous…
The third paper in our series on open source MATLAB / GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation. The main aim of this ongoing work is to develop rapid prototyping techniques…
We propose and analyze discontinuous Galerkin (dG) approximations to 3D-1D coupled systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D centerline. Convergence to weak solutions of a steady state…
In the present paper we consider linear and isotropic Maxwell equations with inhomogeneous interface conditions. We discretize the problem with the discontinuous Galerkin method in space and with the leapfrog scheme in time. An analytical…