Local projection stabilization for advection-diffusion-reaction problems: one-level vs. two-level approach
type: Item
instance of: scholarly article
title: Local projection stabilization for advection-diffusion-reaction problems: one-level vs. two-level approach
zbMATH Open document ID: 1180.65139
author: Gert Lube
author: Petr Knobloch
published in: Applied Numerical Mathematics
publication date: 2009-10-09T00:00:00Z
review text: The authors present a local projection stabilization (LPS) of a finite element method for the linear advection-diffusion-reaction problem \[ Lu:=-\varepsilon \Delta u+{\mathbf b}\cdot\nabla u+\sigma u=f\quad\text{in }\Omega;\qquad u=0\quad \text{on } \partial \Omega, \] where the advection field \({\mathbf b}\) is a finite element solution of an incompressible flow problem. The LPS technique for the numerical solution of transport-dominated probems preserves the stability of methods with residual-based stabilization but has a symmetric form of the stabilization term. The paper contains several novel contributions to the theory of LPS. The authors derive an error estimate showing not only the usual error dependence on the mesh width but also on the polynomial degree of the finite element space and propose a definition of the stabilization parameter depending on the data of the solved problem. Finally the authors observe that the consistency error may deteriorate the convergence order and explain the relation between the LPS method and residual-based stabilization techniques for simplicial finite elements.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5611785
zbMATH Keywords: local projection stabilization
zbMATH Keywords: finite element method
zbMATH Keywords: advection-diffusion-reaction problem
zbMATH Keywords: advection-dominated problem
zbMATH Keywords: stability
zbMATH Keywords: error estimate
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.06.004
OpenAlex ID: W2013301409
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DOI: 10.1016/J.APNUM.2009.06.004
description: scientific article; zbMATH DE number 5611785