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Pure Lagrangian and Semi-Lagrangian Finite Element Methods for the Numerical Solution of Convection-Diffusion Problems

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http://hdl.handle.net/2183/35447
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Title
Pure Lagrangian and Semi-Lagrangian Finite Element Methods for the Numerical Solution of Convection-Diffusion Problems
Author(s)
Benítez, Marta
Bermúdez, Alfredo
Date
2014
Citation
M. Benitez & A. Bermudez. (2014). Pure Lagrangian and Semi-Lagrangian Finite Element Methods for the Numerical Solution of Convection-Diffusion Problems. International Journal of Numerical Analysis and Modeling. 11 (2). 271-287.
Abstract
[Abstract]: In this paper we propose a unified formulation to introduce and analyze (pure) Lagrangian and semi-Lagrangian methods for solving convection-diffusion partial differential equations. This formulation allows us to state classical and new numerical methods. Several examples are given. We combine them with finite element methods for spatial discretization. One of the pure Lagrangian methods we introduce has been analyzed in [4] and [5] where stability and error estimates for time semi-discretized and fully-discretized schemes have been proved. In this paper, we prove new stability estimates. More precisely, we obtain an l∞(H1) stability estimate independent of the diffusion coefficient and, if the underlying flow is incompressible, we get a stability inequality independent of the final time. Finally, the numerical solution of a test problem is presented that confirms the new stability results.
Keywords
Convection-diffusion equation
Pure Lagrangian method
Semi-Lagrangian method
Lagrange-Galerkin methods
Characteristics method
Second order schemes
Finite element method
 
Description
Accepted version.
Editor version
http://www.math.ualberta.ca/ijnam/Volume-11-2014/No-2-14/2014-02-02.pdf
Rights
Version of record: © 2013 Institute for Scientific Computing and Information Accepted version: "Self-archiving involves an embargo period of 12 months. This includes posting the accepted author manuscript on your personal website, private research groups and institutional repositories." https://www.global-sci.org/intro/page/show.html?id=15
ISSN
1705-5105
2617-8710 (e-ISSN)
 

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