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/

Zendy Plus

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

Zendy Tools

Zendy Open

In this paper we investigate a priori error estimates for the space-timeGalerkin finite element discretization of an optimal control problem governedby a simplified linear gradient enhanced damage model. The model equations areof a special structure as the state equation consists of an elliptic PDE whichhas to be fulfilled at almost all times coupled with an ODE that has to holdtrue in almost all points in space. The state equation is discretized by apiecewise constant discontinuous Galerkin method in time and usual conforminglinear finite elements in space. For the discretization of the control weemploy the same discretization technique which turns out to be equivalent to avariational discretization approach. We provide error estimates of optimalorder both for the discretization of the state equation as well as for theoptimal control. Numerical experiments are added to illustrate the proven ratesof convergence.

A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system