A subcell-enriched Galerkin method for advection problems

An hr–adaptive discontinuous Galerkin method for advection–diffusion problems

We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre–processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection–diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed dis...

A Pre–processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection–diffusion–reaction Problems

We propose a pre–processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection–diffusion–reaction problems. Extensive two–dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal–oriented a posteriori error indicators are presented. The example...

Discontinuous Galerkin Methods for Advection-diffusion-reaction Problems

We apply the weighted-residual approach recently introduced in [7] to derive dis-continuous Galerkin formulations for advection-diffusion-reaction problems. We devise the basic ingredients to ensure stability and optimal error estimates in suitable norms, and propose two new methods. 1. Introduction. In recent years Discontinuous Galerkin methods have become increasingly popular, and they have ...

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems

Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales

A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advectiondiffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection-diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domai...