Results 1 
9 of
9
Edge stabilization for Galerkin approximations of convectiondiffusionreaction problems
 Comp. Methods Appl. Mech. Engrg
"... Abstract. We analyze a nonlinear shockcapturing scheme for H 1conforming, piecewiseaffine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions: a local quasiuniformity property and the Xu–Zikatanov condition ensuring that the stiffne ..."
Abstract

Cited by 77 (20 self)
 Add to MetaCart
(Show Context)
Abstract. We analyze a nonlinear shockcapturing scheme for H 1conforming, piecewiseaffine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions: a local quasiuniformity property and the Xu–Zikatanov condition ensuring that the stiffness matrix associated with the Poisson equation is an Mmatrix. A discrete maximum principle is rigorously established in any space dimension for convectiondiffusionreaction problems. We prove that the shockcapturing finite element solution converges to that without shockcapturing if the cell Péclet numbers are sufficiently small. Moreover, in the diffusiondominated regime, the difference between the two finite element solutions superconverges with respect to the actual approximation error. Numerical experiments on test problems with stiff layers confirm the sharpness of the a priori error estimates. 1.
An adaptive stabilized finite element scheme for a water quality model
, 2005
"... Residual type a posteriori error estimators are introduced in this paper for an advectiondiffusionreaction problem with a Dirac delta source term. The error is measured in an adequately weighted W1,pnorm. These estimators are proved to yield global upper and local lower bounds for the correspondi ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Residual type a posteriori error estimators are introduced in this paper for an advectiondiffusionreaction problem with a Dirac delta source term. The error is measured in an adequately weighted W1,pnorm. These estimators are proved to yield global upper and local lower bounds for the corresponding norms of the error. They are used to guide adaptive procedures, which are experimentally shown to lead to optimal orders of convergence.
unknown title
"... On finite element methods for 3D time–dependent convection–diffusion–reaction equations with small diffusion ..."
Abstract
 Add to MetaCart
(Show Context)
On finite element methods for 3D time–dependent convection–diffusion–reaction equations with small diffusion
Edited by
"... A comparison of spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I ..."
Abstract
 Add to MetaCart
(Show Context)
A comparison of spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I
On adaptive anisotropic mesh optimisation for convectiondiffusion problems
, 2012
"... 27/09/2012 On adaptive anisotropic mesh optimisation for convectiondiffusion problems ..."
Abstract
 Add to MetaCart
27/09/2012 On adaptive anisotropic mesh optimisation for convectiondiffusion problems
18 READS
"... On the performance of SOLD methods for convection? diffusion problems with interior layers ..."
Abstract
 Add to MetaCart
On the performance of SOLD methods for convection? diffusion problems with interior layers
121 PUBLICATIONS 2,259 CITATIONS SEE PROFILE
, 2005
"... convectiondiffusionreaction equations: Discrete maximum principle and convergence ..."
Abstract
 Add to MetaCart
(Show Context)
convectiondiffusionreaction equations: Discrete maximum principle and convergence