English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In an earlier paper the last two authors studied spatially semidiscretepiecewise linear finite element approximations of the heat equation and showed that,in the case of the standard Galerkin method, the solution operator of the initial-valueproblem is neither positive nor contractive in the maximum-norm for small time, butthat for the lumped mass method these properties hold, if the triangulations are essentiallyof Delaunay type. In this paper we continue the study by considering fullydiscrete analogues obtained by discretization also in time. The above properties thencarry over to the backward Euler time stepping method, but for other methods theresults are more restrictive. We discuss in particular the θ-method and the (0; 2) Padéapproximation in one space dimension.

On Positivity and Maximum-Norm Contractivity in Time Stepping Methods for Parabolic Equations