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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

A residual error estimator is proposed for the energy norm of the error for ascalar reaction-diffusion problem and for the monodomain model used in cardiacelectrophysiology. The problem is discretized using $P_1$ finite elements inspace, and the backward difference formula of second order (BDF2) in time. Theestimator for space makes use of anisotropic interpolation estimates, assumingonly minimal regularity. Reliability of the estimator is proven under certainmild assumptions on the convergence of the approximate solution. The monodomainmodel couples a nonlinear parabolic partial differential equation (PDE) with anordinary differential equation (ODE) and this setting presents challengestheoretically as well as numerically. A space-time adaptation algorithm isproposed to control the global error, using a non-Euclidean metric for meshadaptation and a simple method to adjust the time step. Numerical examples areused to verify the reliability and efficiency of the estimator, and to test theadaptive algorithm. The potential gains in efficiency of the proposed algorithmcompared to methods using uniform meshes is discussed.

Anisotropic space-time adaptation for reaction-diffusion problems