相关论文: Plane Wave Discontinuous Galerkin methods for scat…
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 investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm can be utilized to improve…
This article introduces a new primal-dual weak Galerkin (PDWG) finite element method for second order elliptic interface problems with ultra-low regularity assumptions on the exact solution and the interface and boundary data. It is proved…
We illustrate a time and memory efficient application of Runge-Kutta discontinuous Galerkin (RKDG) methods for the simulation of the ultrasounds advection in moving fluids. In particular, this study addresses to the analysis of transit-time…
This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial…
Electromagnetic wave scattering from planar dielectric films deposited on one-dimensional, randomly rough, perfectly conducting substrates is studied by numerical simulations for both p- and s-polarization. The reduced Rayleigh equation,…
A universal numerical method is developed for the investigation of magnetic neutron scattering. By applying the pseudospectral-time-domain (PSTD) algorithm to the spinor version of the Schr\"odinger equation, the evolution of the spin-state…
The discontinuous Galerkin (DG) method is widely being used to solve hyperbolic partial differential equations (PDEs) due to its ability to provide high-order accurate solutions in complex geometries, capture discontinuities, and exhibit…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
Standard discontinuous Galerkin methods, based on piecewise polynomials of degree $ \qq=0,1$, are considered for temporal semi-discretization for second order hyperbolic equations. The main goal of this paper is to present a simple and…
We consider a stable unique continuation problem for the wave equation where the initial data is lacking and the solution is reconstructed using measurements in some subset of the bulk domain. Typically fairly sophisticated space-time…
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…
The paper proposes and analyzes an efficient second-order in time numerical approximation for the Allen-Cahn equation, which is a second order nonlinear equation arising from the phase separation model. We firstly present a fully discrete…
Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as \emph{polytopic}) elements have received considerable attention in recent years. Due to the physical frame basis functions…
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker-Planck equations, which admit a gradient flow structure and find application in diverse contexts. The solutions,…
Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equations including many well-known models such as the classical…
Weak Galerkin (WG) refers to general finite element methods for partial differential equations in which differential operators are approximated by weak forms through the usual integration by parts. In particular, WG methods allow the use of…
This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is…
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discrete space, departing from standard discontinuous Trefftz…
We present a stable discontinuous Galerkin (DG) method with a perfectly matched layer (PML) for three and two space dimensional linear elastodynamics, in velocity-stress formulation, subject to well-posed linear boundary conditions. First,…