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

P. Chatzipantelidis ; Z. Horvath ; Vidar Thomée (Institutionen för matematiska vetenskaper, matematik)
Computational Methods in Applied Mathematics (1609-4840). Vol. 15 (2015), 4, p. 417-437.
[Artikel, refereegranskad vetenskaplig]

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.

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

Denna post skapades 2015-10-23.
CPL Pubid: 224734


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Tillämpad matematik

Chalmers infrastruktur