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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article, we present a three-dimensional anisotropic $hp$-meshrefinement strategy for ultraweak discontinuous Petrov--Galerkin (DPG)formulations with optimal test functions. The refinement strategy utilizes thebuilt-in residual-based error estimator accompanying the DPG discretization.The refinement strategy is a two-step process: (a) use the built-in errorestimator to mark and isotropically $hp$-refine elements of the (coarse) meshto generate a finer mesh; (b) use the reference solution on the finer mesh tocompute optimal $h$- and $p$-refinements of the selected elements in the coarsemesh. The process is repeated with coarse and fine mesh being generated inevery adaptation cycle, until a prescribed error tolerance is achieved. Wedemonstrate the performance of the proposed refinement strategy using severalnumerical examples on hexahedral meshes.

An Anisotropic $hp$-Adaptation Framework for Ultraweak Discontinuous Petrov-Galerkin Formulations