In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG)
finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic …

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a
discretization and any element-wise, localizable error estimate, our adaptive method iterates …

We consider the adjoint-based error estimation and goal-oriented mesh refinement for
single and multiple aerodynamic force coefficients as well as residual-based mesh …

In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is
presented for the solution of the incompressible Navier–Stokes equations on staggered …

We propose an efficient, accurate, and robust implicit solver for the incompressible Navier–
Stokes equations, based on a DG spatial discretization and on the TR‐BDF2 method for time …

We deal with the numerical solution of a linear convection-diffusion-reaction equation using
the discontinuous Galerkin method of arbitrary polynomial approximation degree on …

We derive an anisotropic a posteriori error estimate for the adaptive conforming virtual
element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we …

In this work the numerical discretization of the partial differential governing equations for
compressible and incompressible flows is dealt within the discontinuous Galerkin (DG) …

We deal with a numerical solution of nonlinear convection-diffusion problems with the aid of
the discontinuous Galerkin finite element method (DGFEM). We propose a new hp …

The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents
a very challenging computational task, particularly for systems of coupled nonlinear PDEs …