An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDEs

DOI10.1137/18M1208708zbMath1422.49004arXiv1811.09700OpenAlexW2968697191WikidataQ114074291 ScholiaQ114074291MaRDI QIDQ5232312

Gang Chen, John R. Singler, Yangwen Zhang

Publication date: 2 September 2019

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.09700

zbMATH Keywords

error analysisDirichlet boundary controllow regularityhybridizable discontinuous Galerkin (HDG) methodconvection dominated diffusion PDEs

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items (10)

On the Superconvergence of a Hybridizable Discontinuous Galerkin Method for the Cahn–Hilliard Equation ⋮ Bilinear control of convection-cooling: from open-loop to closed-loop ⋮ A hybrid-dG method for singularly perturbed convection-diffusion equations on pipe networks ⋮ A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem ⋮ A new global divergence free and pressure-robust HDG method for tangential boundary control of Stokes equations ⋮ Analysis and Approximations of Dirichlet Boundary Control of Stokes Flows in the Energy Space ⋮ Optimal control of convection-cooling and numerical implementation ⋮ Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system ⋮ $L^\infty$ Norm Error Estimates for HDG Methods Applied to the Poisson Equation with an Application to the Dirichlet Boundary Control Problem ⋮ An MLMCE-HDG method for the convection diffusion equation with random diffusivity

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