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

The purpose of this article is to introduce radial basis function, (RBFs),methods for solving null control problems for the Stokes system with fewinternal scalar controls and Dirichlet or Navier slip boundary conditions. Tothe best of our knowledge, it has not been reported in the literature anynumerical approximation through RBFs to solve the direct Stokes problem withNavier slip boundary conditions. In this paper we fill this gap to show itsapplication for solving the null control problem for the Stokes system. Toachieve this goal, we introduce two radial basis function solvers, one globaland the other local, to discretized the primal and adjoint systems related tothe control problem. Both techniques are based on divergence free global RBFs.Stability analysis for these methods is performed in terms of the spectralradius of the corresponding Gram matrices. By using a conjugate gradientalgorithm, adapted to the radial basis function setting, the control problem issolved. Several test problems in two dimensions are numerically solved by theseRBFs methods to test their feasibility. The solutions to these problems arealso obtained by finite elements techniques, (FE), to compare their relativeperformance.

RBFs methods for null control problems of the Stokes system with Dirichlet and Navier slip boundary conditions