Uniform in $\varepsilon $ discretization error estimates for convection dominated convection-diffusion problems

Error estimates for the convergence of a finite volume discretization of convection-diffusion equations

We study error estimates for a finite volume discretization of an elliptic equation. We prove that, for s ∈ [0,1], if the exact solution belongs to H1+s and the right-hand side is f + div(G) with f ∈ L2 and G ∈ (Hs)N , then the solution of the finite volume scheme converges in discrete H1norm to the exact solution, with a rate of convergence of order hs (where h is the size of the mesh).

Robust DPG Method for Convection-Dominated Diffusion Problems

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...

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...