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On positivity preservation in some finite element methods for the heat equation

Vidar Thomée (Institutionen för matematiska vetenskaper, matematik)
Numerical Methods and Applications. Lecture Notes in Computer Science, 8962 p. 13-24. (2015)

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 study to what extent this property carries over to some piecewise linear finite element discretizations, namely the Standard Galerkin method, the Lumped Mass method, and the Finite Volume Element method. We address both spatially semidiscrete and fully discrete methods.

Nyckelord: Heat equation, Finite element method, Positivity preservation

8th International Conference, NMA 2014, Borovets, Bulgaria, August 20-24, 2014, Revised Selected Papers

Denna post skapades 2015-01-09. Senast ändrad 2015-02-10.
CPL Pubid: 210364


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys

Chalmers infrastruktur