On positivity preservation in some finite element methods for the heat equation
Kapitel i bok, 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.

Finite element method

Positivity preservation

Heat equation

Författare

Vidar Thomee

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Lecture Notes in Computer Science

0302-9743 (ISSN)

13-24

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

DOI

10.1007/978-3-319-15585-2_2

ISBN

978-3-319-15584-5