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On Nonnegativity Preservation in Finite Element Methods for the Heat Equation

Prof. Vidar Thomée, Chalmers University of Technology, Sweden
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Prof. Vidar Thomée, Chalmers University of Technology, Sweden
When Dec 01, 2016
from 04:00 PM to 05:00 PM
Where LH 006
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Abstract:  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 investigate to what extent this property carries over to some piecewise linear finite element discretization methods, namely the Standard Galerkin and the Lumped Mass methods. We study both spatially semidiscrete and fully discrete approximations.

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