# Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems

## Authors

Article

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s10444-004-4142-0

- Cite this article as:
- Casas, E. Adv Comput Math (2007) 26: 137. doi:10.1007/s10444-004-4142-0

- 26 Citations
- 116 Views

## Abstract

We study the numerical approximation of distributed optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Piecewise linear finite elements are used to approximate the control as well as the state. We prove that the *L*^{2}-error estimates are of order o(*h*), which is optimal according with the
\(C^{0,1}(\overline{\Omega})\)
-regularity of the optimal control.

### Keywords

optimal controlsemilinear elliptic equationsnumerical approximationerror estimates## Copyright information

© Springer 2006