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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study semi-Lagrangian schemes for the Dirichlet problem for second-order degenerate elliptic PDEs. Like other wide stencil schemes, these schemes have to be truncated near the boundaries to avoid " over-stepping ". The various modifications proposed in the literature lead to either reduced consistency orders for those points, or even a loss of consistency with the differential operator in the usual sense. We propose a local mesh refinement strategy near domain boundaries which achieves a uniform order of consistency up to the boundary in the first case, and in both cases reduces the width of the region where overstepping occurs, so that the practically observed convergence order is unaffected by overstepping. We demonstrate this numerically for a linear parabolic equation and a second order HJB equation.

Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal Control