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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We develop a cut finite element method for the Bernoulli free boundaryproblem. The free boundary, represented by an approximate signed distancefunction on a fixed background mesh, is allowed to intersect elements in anarbitrary fashion. This leads to so called cut elements in the vicinity of theboundary. To obtain a stable method, stabilization terms is added in thevicinity of the cut elements penalizing the gradient jumps across elementsides. The stabilization also ensures good conditioning of the resultingdiscrete system. We develop a method for shape optimization based on moving thedistance function along a velocity field which is computed as the $H^1$ Rieszrepresentation of the shape derivative. We show that the velocity field is thesolution to an interface problem and we prove an a priori error estimate ofoptimal order, given the limited regularity of the velocity field across theinterface, for the the velocity field in the $H^1$ norm. Finally, we presentillustrating numerical results.

A Cut Finite Element Method for the Bernoulli Free Boundary Value Problem