Related papers: Mapped discontinuous Galerkin interpolations and s…

Improving both accuracy and computational performance of numerical tools is a major challenge for seismic imaging and generally requires specialized implementations to make full use of modern parallel architectures. We present a…

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…

We present a discontinuous Galerkin-finite-difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple.…

In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…

We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these…

Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large-scale wave-propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with non-reflective…

We propose an improved version of the PAMPA algorithm where the solution is sought as globally continuous. The scheme is locally conservative, and there is no mass matrix to invert. This method had been developed in a series of papers, see…

We develop a third-order conservative semi-Lagrangian discontinuous Galerkin (SLDG) scheme for solving linear transport equations on curvilinear unstructured triangular meshes, tailored for complex geometries. To ensure third-order spatial…

We generalise a hybridized discontinuous Galerkin method for incompressible flow problems to non-affine cells, showing that with a suitable element mapping the generalised method preserves a key invariance property that eludes most methods,…

The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in…

We extend the positivity-preserving method of Zhang & Shu (2010, JCP, 229, 3091-3120) to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for…

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with…

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

In this paper, we will develop a class of high order asymptotic preserving (AP) discontinuous Galerkin (DG) methods for nonlinear time-dependent gray radiative transfer equations (GRTEs). Inspired by the work \cite{Peng2020stability}, in…

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind…

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…

The accurate prediction of aerodynamic drag on satellites orbiting in the upper atmosphere is critical to the operational success of modern space technologies, such as satellite-based communication or navigation systems, which have become…

In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic…

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…

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…