Convergence analysis on computation of coupled advection-diffusion-reaction problems

Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts

In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial bounda...

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 ...

Robust a-posteriori estimator for advection-diffusion-reaction problems

We propose an almost-robust residual-based a-posteriori estimator for the advection-diffusion-reaction model problem. The theory is developed in the one-dimensional setting. The numerical error is measured with respect to a norm which was introduced by the author in 2005 and somehow plays the role that the energy norm has with respect to symmetric and coercive differential operators. In particu...

Hierarchical Model (himod) Reduction for Advection-diffusion-reaction Problems

The effective numerical description of challenging problems arising from engineering applications demands often the selection of an appropriate reduced aka ”surrogate” model. The latter should result from a trade-off between reliability and computational affordability (see, e.g., [1, 8]). Different approaches can be pursued to set up the reduced model. In some cases, one can take advantage of s...

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems