Related papers: Stabilization in relation to wavenumber in HDG met…
This paper develops and analyzes some interior penalty discontinuous Galerkin methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in the two and three dimensions. It is…
This paper is concerned with developing efficient numerical methods for acoustic wave scattering in random media which can be expressed as random perturbations of homogeneous media. We first analyze the random Helmholtz problem by deriving…
Superpositions of plane waves are known to approximate well the solutions of the Helmholtz equation. Their use in discretizations is typical of Trefftz methods for Helmholtz problems, aiming to achieve high accuracy with a small number of…
In this paper, we present a hybridized discontinuous Galerkin (HDG) method for Poisson-type problems with sign-changing coefficients. We introduce a sign-changing stabilization parameter that results in a stable HDG method independent of…
In this paper we are concerned with plane wave discontinuous Galerkin (PWDG) methods for Helmholtz equation and time-harmonic Maxwell equations in three-dimensional anisotropic media, for which the coefficients of the equations are matrices…
High order accurate and explicit time-stable solvers are well suited for hyperbolic wave propagation problems. As a result of the complexities of real geometries, internal interfaces and nonlinear boundary and interface conditions,…
We propose Hybridizable Discontinuous Galerkin (HDG) methods for solving the frequency-domain Maxwell's equations coupled to the Nonlocal Hydrodynamic Drude (NHD) and Generalized Nonlocal Optical Response (GNOR) models, which are employed…
We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and…
Local helioseismology comprises of imaging and inversion techniques employed to reconstruct the dynamic and interior of the Sun from correlations of oscillations observed on the surface, all of which require modeling solar oscillations and…
High-frequency wave propagation has many important applications in acoustics, elastodynamics, and electromagnetics. Unfortunately, the finite element discretization for these problems suffers from significant numerical pollution errors that…
We present a study of two residual a posteriori error indicators for the Plane Wave Discontinuous Galerkin (PWDG) method for the Helmholtz equation. In particular we study the h-version of PWDG in which the number of plane wave directions…
In this paper, we present a flux-based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems and propose a new method derived by letting a stabilization parameter tend to infinity. Assuming…
We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…
The recent results presented in arXiv:2202.05608 have led to significant developments in achieving stable approximations of Helmholtz solutions by plane wave superposition. The study shows that the numerical instability and ill-conditioning…
In this paper, we study the stability (in terms of the maximum time step) and accuracy (in terms of the wavenumber-diffusion properties) for several popular discontinuous Galerkin (DG) viscous flux formulations. The considered methods…
The Kelvin-Helmholtz instability serves as a simple, well-defined setup for assessing the accuracy of different numerical methods for solving the equations of hydrodynamics. We use it to extend our previous analysis of the convergence and…
The interaction of light with metallic nanostructures produces a collective excitation of electrons at the metal surface, also known as surface plasmons. These collective excitations lead to resonances that enable the confinement of light…
The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite elements, in DG methods, numerical fluxes are used to…
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…
We analyse numerical errors (dissipation and dispersion) introduced by the discretisation of inviscid and viscous terms in energy stable discontinuous Galerkin methods. First, we analyse these methods using a linear von Neumann analysis…