Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d
Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d
View/Date of Publication
06.2016Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
Show full item record
Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11849
Abstract
We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on precomputed fine-scale correctors. The exponential decay of these correctors and their localisation to local patch problems, which depend on the direction of the velocity field and the singular perturbation parameter, is rigorously justified. Under moderate assumptions, this stabilization guarantees stability and quasi-optimal rate of convergence for arbitrary mesh Péclet numbers on fairly coarse meshes at the cost of additional inter-element communication.
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1093/imanum/drx027Part of Series
INS Preprints ; 1612Li, Guanglian; Peterseim, Daniel; Schedensack, Mira: Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d. In: INS Preprints, 1612.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11849
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11849
@unpublished{handle:20.500.11811/11849,
author = {{Guanglian Li} and {Daniel Peterseim} and {Mira Schedensack}},
title = {Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = jun,
INS Preprints},
volume = 1612,
note = {We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on precomputed fine-scale correctors. The exponential decay of these correctors and their localisation to local patch problems, which depend on the direction of the velocity field and the singular perturbation parameter, is rigorously justified. Under moderate assumptions, this stabilization guarantees stability and quasi-optimal rate of convergence for arbitrary mesh Péclet numbers on fairly coarse meshes at the cost of additional inter-element communication.},
url = {https://hdl.handle.net/20.500.11811/11849}
}
author = {{Guanglian Li} and {Daniel Peterseim} and {Mira Schedensack}},
title = {Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = jun,
INS Preprints},
volume = 1612,
note = {We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on precomputed fine-scale correctors. The exponential decay of these correctors and their localisation to local patch problems, which depend on the direction of the velocity field and the singular perturbation parameter, is rigorously justified. Under moderate assumptions, this stabilization guarantees stability and quasi-optimal rate of convergence for arbitrary mesh Péclet numbers on fairly coarse meshes at the cost of additional inter-element communication.},
url = {https://hdl.handle.net/20.500.11811/11849}
}
The following license files are associated with this item:
