In this paper, we present a novel class of high-order Runge–Kutta (RK) discontinuous
Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond …

The space–time adaptive ADER–DG finite element method with LST–DG predictor and a
posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of …

This paper presents eigensolution and non-modal analyses for immersed boundary
methods (IBMs) based on volume penalization for the linear advection equation. This …

When the discontinuous Galerkin (DG) method is applied to hyperbolic problems in two
dimensions on triangular meshes and paired with an explicit time integration scheme, an …

The space-time adaptive ADER finite element DG method with a posteriori correction
technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to …

We derive explicit expressions for the eigenvalues (spectrum) of the discontinuous Galerkin
spatial discretization applied to the linear advection equation. We show that the eigenvalues …

Discontinuous Galerkin (DG) and central DG methods are two related families of finite
element methods. They can provide high order spatial discretizations that are often …

Numerical methods of the ADER family, in particular finite-element ADER-DG and finite-
volume ADER-WENO methods, are among the most accurate numerical methods for solving …

In engineering applications, discontinuous Galerkin methods (DG) have been proven to be a
powerful and flexible class of high order methods for problems in computational fluid …

In this paper, we compare the semi-discrete behavior of several numerical methods
including the Discontinuous Galerkin (DG), classical Finite Difference (FD), Dispersion …