A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity
In the first part of this work, we analyzed an unconstrained Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D convex polygonal domain, we also proved an optimal superlinear convergence rate for the control under certain assumptions on the domain and on the target state. In this work, we revisit the convergence analysis without these assumptions; in this case, the solution can have low regularity, and we use a different analysis approach. We again prove an optimal convergence rate for the control and present numerical results to illustrate the convergence theory.
W. Gong et al., "A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity," SIAM Journal on Numerical Analysis, vol. 56, no. 4, pp. 2262-2287, Society for Industrial and Applied Mathematics Publications, Jul 2018.
The definitive version is available at https://doi.org/10.1137/17M1152103
Mathematics and Statistics
Keywords and Phrases
Diffusion in liquids; Error analysis; Heat convection; Convection diffusion; Convergence analysis; Convex polygonal domain; Dirichlet boundary controls; Discontinuous galerkin; Discontinuous Galerkin methods; Low regularity; Superlinear convergence rate; Galerkin methods; Hybridizable discontinuous Galerkin method (HDG)
International Standard Serial Number (ISSN)
Article - Journal
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01 Jul 2018