Related papers: On perfectly matched layers for discontinuous Petr…
This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and…
A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…
In the numerical simulation of ideal MHD, keeping the pressure and density positive is essential for both physical considerations and numerical stability. This is a challenge, due to the underlying relation between such…
The perfectly matched layer (PML) is a very popular tool in the truncation of wave scattering in unbounded domains. In Chandler-Wilde & Monk et al. 2009, the author proposed a conjecture that for scattering problems with rough surfaces, the…
We consider DPG methods with optimal test functions and broken test spaces based on ultra-weak formulations of general second order elliptic problems. Under some assumptions on the regularity of solutions of the model problem and its…
We introduce a new level-set shape optimization approach based on polytopic (i.e., polygonal in two and polyhedral in three spatial dimensions) discontinuous Galerkin methods. The approach benefits from the geometric mesh flexibility of…
This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…
The purpose of the present paper is to compare two semi-Lagrangian methods in the context of the four-dimensional Vlasov--Poisson equation. More specifically, our goal is to compare the performance of the more recently developed…
We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dimer lattice of topological resonators. We examine the…
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions…
We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable…
We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lam\'e system of linear elasticity in polyhedral domains in $\mathbb{R}^3$. In order to resolve possible corner, edge, and corner-edge singularities,…
In this paper, we design a truly exact and optimal perfect absorbing layer (PAL) for domain truncation of the two-dimensional Helmholtz equation in an unbounded domain with bounded scatterers. This technique is based on a complex…
A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed for solving time-harmonic scalar wave propagation problems. This method relies on a standard discontinuous Galerkin scheme with upwind numerical fluxes and…
We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The…
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…
An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method…
The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with non-symmetric functional settings (different infinite-dimensional trial and test…
We provide a mathematical framework for studying different versions of discontinuous Galerkin (DG) approaches for solving 2D Riemann-Liouville fractional elliptic problems on a finite domain. The boundedness and stability analysis of the…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…