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A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEs.
- Source :
- Numerische Mathematik; Feb2020, Vol. 144 Issue 2, p375-411, 37p
- Publication Year :
- 2020
-
Abstract
- We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. These problems can involve atypical variational formulations, and often have solutions with low regularity on polyhedral domains. These issues can provide challenges for numerical methods and the associated numerical analysis. We propose an HDG method for a Dirichlet boundary control problem for the Poisson equation, and obtain optimal a priori error estimates for the control. Specifically, under certain assumptions, for a 2D convex polygonal domain we show the control converges at a superlinear rate. We present 2D and 3D numerical experiments to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]
- Subjects :
- GALERKIN methods
CONVEX domains
NUMERICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 0029599X
- Volume :
- 144
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Numerische Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 141453721
- Full Text :
- https://doi.org/10.1007/s00211-019-01090-2