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

Kolmogorov $n$-widths and low-rank approximations are studied for families ofelliptic diffusion PDEs parametrized by the diffusion coefficients. The decayof the $n$-widths can be controlled by that of the error achieved by best$n$-term approximations using polynomials in the parametric variable. However,we prove that in certain relevant instances where the diffusion coefficientsare piecewise constant over a partition of the physical domain, the $n$-widthsexhibit significantly faster decay. This, in turn, yields a theoreticaljustification of the fast convergence of reduced basis or POD methods whentreating such parametric PDEs. Our results are confirmed by numericalexperiments, which also reveal the influence of the partition geometry on thedecay of the $n$-widths.

Kolmogorov widths and low-rank approximations of parametric elliptic PDEs