On positivity preservation in some finite element methods for the heat equation
Paper i proceeding, 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.

Heat equation

Finite element method

Positivity preservation


Vidar Thomee

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 8962 13-24
978-331915584-5 (ISBN)

8th International Conference on Numerical Methods and Applications, NMA 2014
Borovets, Bulgaria,




Grundläggande vetenskaper



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