Sharp error estimates for a finite element-penalty approach to a class of regulator problems Academic Article uri icon

abstract

  • Quadratic cost optimal controls can be solved by penalizing the governing linear differential equation [2], [9]. In this paper, we study the numerical analysis of this approach using finite elements. We formulate the geometric condition (H) which requires that pairs of certain related finite-dimensional approximation spaces form "angles" which are bounded away from the "180° angle". Under condition (H), we prove that the penalty parameter and the discretization parameter h are independent in the error bounds, thereby giving sharp asymptotic error estimates. This condition (H) is shown to be also a necessary condition for such independence. Examples and numerical evidence are also provided. © 1983 American Mathematical Society.

author list (cited authors)

  • Chen, G., Mills, W. H., Sun, S. H., & Yost, D. A.

citation count

  • 2

publication date

  • January 1983