The finite element method with weighted basis functions for singularly perturbed convection-diffusion problems
type: Item
instance of: scholarly article
title: The finite element method with weighted basis functions for singularly perturbed convection-diffusion problems
zbMATH Open document ID: 1083.65106
author: Sumit K. Garg
published in: Journal of Computational Physics
publication date: 2004-08-06T00:00:00Z
review text: A convection diffusion equation containing a small parameter at the high order derivative is considered. A finite element method using specially designed basis functions is proposed. These basis functions are obtained by means of multiplying the standard basis functions by a suitable weight. Properties of the basis functions are studied in one and two dimensions. Based on the properties of these basis functions a special technique is developed for approximating of fluxes. The approximate fluxes are used in the computation of the stiffness matrix in order to reduce the computational cost. Numerical results are given in one and two space dimensions.
reviewed by: Ramaz Botchorishvili
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 2083223
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: singular perturbation
zbMATH Keywords: unstructured mesh
zbMATH Keywords: weighted basis functions
zbMATH Keywords: finite element method
zbMATH Keywords: flux approximation
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.jcp.2003.10.028
OpenAlex ID: W1984791114
Wikidata QID: Q59416210
cites work: Stability and Error Estimates of Galerkin Finite Element Approximations for Convection—Diffusion Equations
cites work: Some upwinding techniques for finite element approximations of convection-diffusion equations
cites work: Q3857931
cites work: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
cites work: Finite element methods for second order differential equations with significant first derivatives
cites work: Upwinding of high order Galerkin methods in conduction−convection problems
cites work: The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
cites work: TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
cites work: On the approximation of convection problems in fluid dynamics
cites work: Quadratic finite element schemes for two-dimensional convective-transport problems
cites work: Q3877290
cites work: Q3862348
cites work: Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
cites work: A simple scheme for developing ‘upwind’ finite elements
cites work: Q3857926
cites work: Q3994952
cites work: Q4486278
cites work: A new non-conforming Petrov-Galerkin finite-element method with triangular elements for a singularly perturbed advection-diffusion problem
cites work: An exponentially fitted finite volume method for the numerical solution of 2D unsteady incompressible flow problems
cites work: A Globally Uniformly Convergent Finite Element Method for a Singularly Perturbed Elliptic Problem in Two Dimensions
cites work: Layer-Adapted Grids for Singular Perturbation Problems
cites work: Q4871736
cites work: A finite element method for a singularly perturbed boundary value problem
cites work: An Analysis of a Singularly Perturbed Two-Point Boundary Value Problem Using Only Finite Element Techniques
cites work: Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
cites work: A novel exponentially fitted triangular finite element method for an advection-diffusion problem with boundary layers
cites work: An analysis of a conforming exponentially fitted finite element method for a convection-diffusion problem
cites work: A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation
cites work: A monotone finite element scheme for convection-diffusion equations
DOI: 10.1016/J.JCP.2003.10.028
description: scientific article; zbMATH DE number 2083223