Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients

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 ...

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...

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems

A Schwarz Waveform Relaxation Method for Advection–Diffusion–Reaction Problems with Discontinuous Coefficients and non-Matching Grids

We present a non-overlapping Schwarz waveform relaxation method for solving advection-reaction-diffusion problems in heterogeneous media. The domain decomposition method is global in time, which permits the use of different time steps in different subdomains. We determine optimal non-local, and optimized Robin transmission conditions. We also present a space-time finite volume scheme especially...

A Robin–Robin preconditioner for advection–diffusion equations with discontinuous coefficients

We consider an advection–diffusion problem with discontinuous viscosity coefficients. We apply a substructuring technique and we extend to the resulting Schur complement the Robin–Robin preconditioner used for problems with constant viscosity. A quasi optimal convergence analysis is performed in the case of uniform convection by means of Fourier techniques. The variational formulation in order ...