Related papers: Reconstructed discontinuous Galerkin method for co…
We present unconditionally energy stable Runge-Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our algorithm is geared toward arbitrarily high order approximations in both space and time,…
In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier-Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with…
In this work a solver for instationary two-phase flows on the basis of the extended Discontinuous Galerkin (extended DG/XDG) method is presented. The XDG method adapts the approximation space conformal to the position of the interface. This…
In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet…
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is…
In this paper, we present consistent and inconsistent discontinuous Galerkin methods for incompressible Euler and Navier-Stokes equations with the kinematic pressure, Bernoulli function and EMAC function. Semi- and fully discrete energy…
We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8, 9, 19, 21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across…
We propose a globally divergence conforming discontinuous Galerkin (DG) method on Cartesian meshes for {\em curl-type hyperbolic conservation} laws based on directly evolving the face and cell moments of the Raviart-Thomas approximation…
A novel class of Runge-Kutta discontinuous Galerkin schemes for coupled systems of conservation laws in multiple space dimensions that are separated by a fixed sharp interface is introduced. The schemes are derived from a relaxation…
This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schr\"odinger equation with the wave operator. The focus of the study is on the energy-conserving or energy-dissipating behavior of the method with…
This paper presents a conservative discontinuous Galerkin method for the simulation of supercritical and transcritical real-fluid flows without phase separation. A well-known issue associated with the use of fully conservative schemes is…
In this second part of our two-part paper, we extend to multiple spatial dimensions the one-dimensional, fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme developed in the first part for the…
In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG)…
In this work, we develop an efficient high order discontinuous Galerkin (DG) method for solving the Electrical Impedance Tomography (EIT). EIT is a highly nonlinear ill-posed inverse problem where the interior conductivity of an object is…
This work aims at presenting a Discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated…
In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…
We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin formulation that corrects the standard Galerkin…
Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while, with the aid of limiters, still resolving strong shocks. These and other properties make DG methods…
Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness…
We present a discontinuous Galerkin method for moist atmospheric dynamics, with and without warm rain. By considering a combined density for water vapour and cloud water, we avoid the need to model and compute a source term for…