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 present a reduced basis method for parametrized partial differential equations certified by a dual-norm bound of the residual computed not in the typical finite-element "truth" space but rather in an infinite-dimensional function space. The bound builds on a finite element method and an associated reduced-basis approximation derived from a minimum-residual mixed formulation. The offline stage combines a spatial mesh adaptation for finite elements and a greedy parameter sampling strategy for reduced bases to yield a reliable online system in an efficient manner; the online stage provides the solution and the associated dual-norm bound of the residual for any parameter value in complexity independent of the finite element resolution. We assess the effectiveness of the approach for a parametrized reaction-diffusion equation and a parametrized advection-diffusion equation with a corner singularity; not only does the residual bound provide reliable certificates for the solutions, the associated mesh adaptivity significantly reduces the offline computational cost for the reduced-basis generation and the greedy parameter sampling ensures quasi-optimal online complexity.

A minimum-residual mixed reduced basis method: Exact residual certification and simultaneous finite-element reduced-basis refinement