Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year


IMPACT FACTOR 2016: 1.097

CiteScore 2016: 1.09

SCImago Journal Rank (SJR) 2016: 0.872
Source Normalized Impact per Paper (SNIP) 2016: 0.887

Mathematical Citation Quotient (MCQ) 2015: 0.68

Online
ISSN
1609-9389
See all formats and pricing
In This Section
Volume 15, Issue 4 (Oct 2015)

Issues

On Preservation of Positivity in Some Finite Element Methods for the Heat Equation

Panagiotis Chatzipantelidis
  • Corresponding author
  • Department of Mathematics and Applied Mathematics, University of Crete, GR-70013 Heraklion, Greece
  • Email:
/ Zoltan Horváth
  • Department of Mathematics and Computational Sciences, Széchenyi István University, 1 Egyetem Square, H-9026 Györ, Hungary
  • Email:
/ Vidar Thomée
  • Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-41296 Göteborg, Sweden; and Institute of Applied and Computational Mathematics, FORTH, GR-71110 Heraklion, Greece
  • Email:
Published Online: 2015-08-04 | DOI: https://doi.org/10.1515/cmam-2015-0018

Abstract

We consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We complement in a number of ways earlier studies of the possible extension of this fact to spatially semidiscrete and fully discrete piecewise linear finite element discretizations, based on the standard Galerkin method, the lumped mass method, and the finite volume element method. We also provide numerical examples that illustrate our findings.

Keywords: Heat Equation; Finite Element Method; Lumped Mass; Finite Volume Element Method; Spatially Semidiscrete; Fully Discrete; Positivity Preserving; Finite Element Discretization

MSC: 65M12; 65M60

About the article

Received: 2015-02-11

Revised: 2015-06-21

Accepted: 2015-06-29

Published Online: 2015-08-04

Published in Print: 2015-10-01


Funding Source: University of Crete Research Committee

Award identifier / Grant number: KA 4179

Funding Source: European Social Fund and the government of Hungary

Award identifier / Grant number: TÁMOP-4.2.2.A-11/1/KONV-2012-0012


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0018.

Export Citation

© 2015 by De Gruyter. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in