Error estimates for the numerical approximation of Neumann control problems |
| |
Authors: | Eduardo Casas Mariano Mateos |
| |
Institution: | (1) Dpto. de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39071 Santander, Spain;(2) Dpto. de Matemáticas, E.P.S.I. de Gijón, Universidad de Oviedo, Campus de Viesques, 33203 Gijon, Spain |
| |
Abstract: | We continue the discussion of error estimates for the numerical analysis of Neumann boundary control problems we started in
Casas et al. (Comput. Optim. Appl. 31:193–219, 2005). In that paper piecewise constant functions were used to approximate the control and a convergence of order O(h) was obtained. Here, we use continuous piecewise linear functions to discretize the control and obtain the rates of convergence
in L
2(Γ). Error estimates in the uniform norm are also obtained. We also discuss the approach suggested by Hinze (Comput. Optim.
Appl. 30:45–61, 2005) as well as the improvement of the error estimates by making an extra assumption over the set of points corresponding to
the active control constraints. Finally, numerical evidence of our estimates is provided.
The authors were supported by Ministerio de Ciencia y Tecnología (Spain). |
| |
Keywords: | Boundary control Semilinear elliptic equation Numerical approximation Error estimates |
本文献已被 SpringerLink 等数据库收录! |
|