Stabilized finite element methods for singularly perturbed parabolic problems
type: Item
instance of: scholarly article
title: Stabilized finite element methods for singularly perturbed parabolic problems
zbMATH Open document ID: 0838.65095
DOI: 10.1016/0168-9274(95)00024-O
author: Yanyan Li
published in: Applied Numerical Mathematics
publication date: 1996-06-09T00:00:00Z
review text: The authors consider two stabilized numerical schemes for solving Dirichlet-type initial-boundary value problems of the parabolic equation \((\partial_t + L_\varepsilon) u : = \partial_t u - \varepsilon \Delta u + b \cdot \nabla u + cu = f\), modelling convection-reaction-diffusion. Weighted least squares forms of the underlying equation are added to the basic Galerkin finite element semidiscretization in order to accomodate the method to (possibly locally varying) convective, reactive or diffusive terms. Time integration is performed with standard stable one-step methods. Stability and error estimates are derived on unstructured grids and the design of the numerical damping parameters are considered. Numerical results are given for typical model problems, including ``translating cone''.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 817335
zbMATH Keywords: parabolic system
zbMATH Keywords: long time behavior
zbMATH Keywords: stability
zbMATH Keywords: numerical results
zbMATH Keywords: convection-reaction-diffusion equation
zbMATH Keywords: singular perturbation
zbMATH Keywords: Galerkin finite element semidiscretization
zbMATH Keywords: one-step methods
zbMATH Keywords: error estimates
reviewed by: Akira Kaneko
MaRDI profile type: Publication
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full work available at URL: 0168-9274(95)00024-o
OpenAlex ID: W2091684284
description: scientific article; zbMATH DE number 817335