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

We propose a monotone discretization for the integral fractional Laplaceequation on bounded Lipschitz domains with the homogeneous Dirichlet boundarycondition. The method is inspired by a quadrature-based finite differencemethod of Huang and Oberman, but is defined on unstructured grids in arbitrarydimensions with a more flexible domain for approximating singular integral. Thescale of the singular integral domain not only depends on the local grid size,but also on the distance to the boundary, since the H\"{o}lder coefficient ofthe solution deteriorates as it approaches the boundary. By using a discretebarrier function that also reflects the distance to the boundary, we showoptimal pointwise convergence rates in terms of the H\"{o}lder regularity ofthe data on both quasi-uniform and graded grids. Several numerical examples areprovided to illustrate the sharpness of the theoretical results.

A monotone discretization for integral fractional Laplacian on bounded Lipschitz domains: Pointwise error estimates under H\"{o}lder regularity