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 propose and investigate the application of alternative enriched test spaces in the discontinuous Petrov–Galerkin (DPG) finite element framework for singular perturbation linear problems, with an emphasis on 2D convection-dominated diffusion. Providing robustL  2{L^{2}}    error estimates for the field variables is considered a convenient feature for this class of problems, since this norm would not account for the large gradients present in boundary layers. With this requirement in mind, Demkowicz and others have previously formulated special test norms, which through DPG deliver the desiredL  2{L^{2}}    convergence. However, robustness has only been verified through numerical experiments for  tailored  test norms which are problem-specific, whereas the  quasi-optimal  test norm (not problem specific) has failed such tests due to the difficulty to resolve the optimal test functions sought in the DPG technology. To address this issue (i.e. improve optimal test functions resolution for the quasi-optimal test norm), we propose to discretize the local test spaces with functions that depend on the perturbation parameter ϵ. Explicitly, we work with B-spline spaces defined on an ϵ-dependent Shishkin submesh. Two examples are run using adaptive  h -refinement to compare the performance of proposed test spaces with that of standard test spaces. We also include a modified norm and a continuation strategy aiming to improve time performance and briefly experiment with these ideas.

Alternative Enriched Test Spaces in the DPG Method for Singular Perturbation Problems