Related papers: Local Discontinuous Galerkin Methods for Solving C…
In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…
We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered and structured meshes. By combining spatial staggering with local time-stepping near boundaries, the method overcomes the…
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…
This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection-diffusion-reaction problems discretized by Galerkin or…
Explicit, unconditionally stable, high-order schemes for the approximation of some first- andsecond-order linear, time-dependent partial differential equations (PDEs) are proposed.The schemes are based on a weak formulation of a…
We study the high-order local discontinuous Galerkin (LDG) method for the $p$-Laplace equation. We reformulate our spatial discretization as an equivalent convex minimization problem and use a preconditioned gradient descent method as the…
In this paper, a fully discrete local discontinuous Galerkin (LDG) finite element method is considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation. The scheme is based on a finite difference method in time and local…
We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general…
We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main…
The aim of this paper is to apply a high-order discontinuous-in-time scheme to second-order hyperbolic partial differential equations (PDEs). We first discretize the PDEs in time while keeping the spatial differential operators…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
We apply the Local Discontinuous Galerkin discretisation to flow equations of the O(N)-model in the Local Potential Approximation. The improved stability is directly observed by solving the flow equation for various $N$ and space-time…
An energy conservative discontinuous Galerkin scheme for a generalised third order KdV type equation is designed. Based on the conservation principle, we propose techniques that allow for the derivation of optimal a priori bounds for the…
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 apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to…
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the…
In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…
An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the inter-element fluxes, and both…