Optimal Convergence Analysis for Convection Dominated Diffusion Problems

Robust DPG Method for Convection-Dominated Diffusion Problems

Equidistribution grids for two-parameter convection–diffusion boundary-value problems

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

A Nonlinear Subgrid–Scale Model for Convection Dominated, Convection Diffusion Problems

We present a nonlinear subgrid–scale method for the stabilization of the Galerkin approximation to convection dominated, convection diffusion problems, establish existence and uniqueness results, and provide an a priori error estimate for the method. ∗email: [email protected], Department of Mathematical Sciences, Clemson University, Clemson S.C. 29634 †email: [email protected], Department of...

On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convectiondominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). F...

Discontinuous Galerkin Methods for Convection-Dominated Problems

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the m...