Abstract
The main purpose in this chapter is to discuss stability and smoothness estimates for the semidiscrete solution of the homogeneous heat equation with respect to the maximum-norm, and some consequences of such estimates for error bounds for problems with smooth and nonsmooth initial data. The semidiscrete solution is sought in a piecewise linear finite element space belonging to a quasiuniform family.
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© 2006 Springer
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Thomée, V. (2006). Maximum-Norm Estimates and Analytic Semigroups. In: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33122-0_6
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DOI: https://doi.org/10.1007/3-540-33122-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33121-6
Online ISBN: 978-3-540-33122-3
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