Analysis of a Hybridizable Discontinuous Galerkin Scheme for the Tangential Control of the Stokes System

Abstract

We consider an unconstrained tangential Dirichlet boundary control problem for the Stokes equations with an L2 penalty on the boundary control. The contribution of this paper is twofold. First, we obtain well-posedness and regularity results for the tangential Dirichlet control problem on a convex polygonal domain. The analysis contains new features not found in similar Dirichlet control problems for the Poisson equation; an interesting result is that the optimal control has higher local regularity on the individual edges of the domain compared to the global regularity on the entire boundary. Second, we propose and analyze a hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For convex polygonal domains, our theoretical convergence rate for the control is optimal with respect to the global regularity on the entire boundary. We present numerical experiments to demonstrate the performance of the HDG method.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Comments

National Science Foundation, Grant DMS-1619904

Keywords and Phrases

Hybridizable discontinuous Galerkin method; Stokes equations; Tangential Dirichlet boundary control

International Standard Serial Number (ISSN)

0764-583X; 1290-3841

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 EDP Sciences, All rights reserved.

Publication Date

01 Nov 2020

Link to Full Text

Share

 
COinS