Related papers: On discontinuous Galerkin discretizations of secon…
This paper investigates superconvergence properties of the local discontinuous Galerkin methods with generalized alternating fluxes for one-dimensional linear convection-diffusion equations. By the technique of constructing some special…
This paper develops interior penalty discontinuous Galerkin (IP-DG) methods to approximate $W^{2,p}$ strong solutions of second order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients.…
This paper develops a discontinuous Galerkin (DG) finite element differential calculus theory for approximating weak derivatives of Sobolev functions and piecewise Sobolev functions. By introducing numerical one-sided derivatives as…
The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can, e.g., be done by backward difference formulae (BDF) or…
Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares. This…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
A singularly perturbed convection-diffusion problem posed on the unit square in $\mathbb{R}^2$, whose solution has exponential boundary layers, is solved numerically using the local discontinuous Galerkin (LDG) method with piecewise…
In this paper, we generalize a high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for multi-dimensional linear transport equations without operator splitting developed in Cai et al. (J. Sci. Comput. 73: 514-542, 2017) to the…
This paper develops three high-order accurate discontinuous Galerkin (DG) methods for the one-dimensional (1D) and two-dimensional (2D) nonlinear Dirac (NLD) equations with a general scalar self-interaction. They are the Runge-Kutta DG…
In this paper, we theoretically and numerically verify that the discontinuous Galerkin (DG) methods with central fluxes for linear hyperbolic equations on non-uniform meshes have sub-optimal convergence properties when measured in the…
Second Moment Methods (SMMs) are developed that are consistent with the Discontinuous Galerkin (DG) spatial discretization of the discrete ordinates (or \Sn) transport equations. The low-order (LO) diffusion system of equations is…
We extend the discontinuous Galerkin (DG) framework to the analysis of first-order hyperbolic and advection-dominated problems posed on implicitly defined surfaces. The focus will be on the hyperbolic part, which is discretised using a…
An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution…
We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…
We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the…
The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ($-1<\alpha<0$) or wave ($0<\alpha<1$) equation. A numerical solution is found by applying a…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…