A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimal Control Problems with Measure Data
作者: Pratibha ShakyaRajen Kumar Sinha
作者单位: 1Department of Mathematics , Indian Institute of Technology Guwahati , Guwahati , India
刊名: Numerical Functional Analysis and Optimization, 2020, Vol.41 (2), pp.158-191
来源数据库: Taylor & Francis Journal
DOI: 10.1080/01630563.2019.1615948
关键词: Parabolic optimal control problemMeasure data in spaceFinite element methodSpatially discrete problemFully discrete problemA priori error estimates
原始语种摘要: Abstract(#br)We study finite element approximations of parabolic optimal control problem with measure data in space in a bounded convex domain. The main mathematical difficulty of this kind of problem is low regularity of the solution of the state equation due to the presence of measure data in source term. This introduces some difficulties in both theory and numerics of finite element error analysis. We first prove the existence, uniqueness and regularity of the solution to the control problem. A priori error estimates for the state and control variables are derived for both the spatially discrete and fully discrete approximations of optimal control problems. Moreover, convergence...
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关键词翻译
关键词翻译
  • problem 题目
  • optimal 最佳的
  • control 控制
  • variables 变量
  • piecewise 分段
  • element 元素
  • state 状态
  • bounded 有界的
  • error 误差
  • prove 实验