Related papers: Hybridized discontinuous Galerkin methods for wave…
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time,…
This paper presents high-order, well-balanced, path-conservative discontinuous Galerkin (DG) methods for the shallow water linearized moment equations (SWLME), designed to preserve both still and moving water equilibrium states. Unlike the…
This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous.…
In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…
We propose a new formula for the nonlinear viscous numerical flux and extend the direct discontinuous Galerkin method with interface correction (DDGIC) of Liu and Yan (H. Liu, J. Yan, The direct discontinuous Galerkin (DDG) method for…
In this paper, a new stabilized discontinuous Galerkin method within a new function space setting is introduced, which involves an extra stabilization term on the normal fluxes across the element interfaces. It is different from the general…
Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations…
We develop a multi-dimensional hybrid discontinuous Galerkin method for multi-scale kinetic equations. This method is based on moment realizability matrices, a concept introduced by D. Levermore, W. Morokoff and B. Nadiga for one…
We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed formulation which immediately allows us to compute the…
Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…
A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid FEMs,discontinuous Galerkin (DG) methods, hybrid…
This paper is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary…
In this paper, we perform non-linear minimization using the Hybridizable Discontinuous Galerkin method (HDG) for the discretization of the forward problem, and implement the adjoint-state method for the computation of the functional…
We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and…
In this paper, we study superconvergence properties of the discontinuous Galerkin (DG) method for one-dimensional linear hyperbolic equation when upwind fluxes are used. We prove, for any polynomial degree $k$, the $2k+1$th (or $2k+1/2$th)…
We generalize the energy-based discontinuous Galerkin method proposed in [SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave equations. A stability and convergence analysis is presented along with numerical…
We introduce and analyze a discontinuous Galerkin method for a time-harmonic eddy current problem formulated in terms of the magnetic field. The scheme is obtained by putting together a DG method for the approximation of the vector field…
In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the corresponding differential operator. We propose a new…
The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem…
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…