Error analysis of an HDG method for a distributed optimal control problem

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• 作者：Huiqing Zhu^a ; ^{Huiqing.Zhu@usm.edu" class="auth_mail" title="E-mail the corresponding author} ; Fatih Celiker^b ; ^{celiker@math.wayne.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：49K20 ; 49M25 ; 65J10 ; 65N15
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：307
• 期：Complete
• 页码：2-12
• 全文大小：431 K

文摘

In this paper, we present a priori   error analysis of a hybridizable discontinuous Galerkin (HDG) method for a distributed optimal control problem governed by diffusion equations. The error estimates are established based on the projection-based approach recently used to analyze these methods for the diffusion equation. We proved that for approximations of degree k$k$ on conforming meshes, the orders of convergence of the approximation to fluxes and scalar variables are k+1$k+1$ when the local stabilization parameter is suitably chosen.