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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the stability of explicit Runge-Kutta methods for high orderLagrangian finite element approximation of linear parabolic equations andestablish bounds on the largest eigenvalue of the system matrix whichdetermines the largest permissible time step. A bound expressed in terms of theratio of the diagonal entries of the stiffness and mass matrices is shown to betight within a small factor which depends only on the dimension and the choiceof the reference element and basis functions but is independent of the mesh orthe coefficients of the initial-boundary value problem under consideration.Another bound, which is less tight and expressed in terms of mesh geometry,depends only on the number of mesh elements and the alignment of the mesh withthe diffusion matrix. The results provide an insight into how the interplaybetween the mesh geometry and the diffusion matrix affects the stability ofexplicit integration schemes when applied to a high order finite elementapproximation of linear parabolic equations on general nonuniform meshes.

Stability of explicit Runge-Kutta methods for high order finite element approximation of linear parabolic equations