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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We propose a hybridizable discontinuous Galerkin (HDG) method to approximatethe solution of a tangential Dirichlet boundary control problem for the Stokesequations with an $ L^2 $ penalty on the boundary control. The contribution ofthis paper is twofold. First, we obtain well-posedness and regularity resultsfor the tangential Dirichlet control problem on a convex polygonal domain. Theanalysis contains new features not found in similar Dirichlet control problemsfor the Poisson equation; an interesting result is that the optimal control hashigher local regularity on the individual edges of the domain compared to theglobal regularity on the entire boundary. Second, under certain assumptions onthe domain and the target state, we prove a priori error estimates for thecontrol for the HDG method. In the 2D case, our theoretical convergence ratefor the control is superlinear and optimal with respect to the globalregularity on the entire boundary. We present numerical experiments todemonstrate the performance of the HDG method.

An HDG Method for Tangential Boundary Control of Stokes Equations I: High Regularity