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

Author

Vidar Thomee

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

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

03029743 (ISSN) 16113349 (eISSN)

13-24

Subject Categories

Computational Mathematics

Roots

Basic sciences

DOI

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

ISBN

978-3-319-15584-5

More information

Created

10/7/2017