Numerical analysis, optimal control of PDEs, inverse problems.
My current research is on the analysis and numerical analysis of inverse and optimal control problems with PDE and variational inequality constraints. I have worked on analysing algorithms for a phase field approach to binary image recovery, and implemented them in DUNE-FEM. More recently I have worked on mesh adaptivity for optimal control of variational inequalities, and on proving convergence for finite element discretisations of problems related to the optimal control of PDEs with sparse data.
Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state. C. Brett, C. M. Elliott, M. Hintermüller, C. Löbhard. (Submitted to Interfaces and Free Boundaries).
Phase field methods for binary recovery. C. Brett, A. S. Dedner, C. M. Elliott. (Accepted in ESF OPTPDE Proceedings).
Accuracy and stability of filters for dissipative PDEs. C. Brett, K. F. Lam, K. J . H. Law, D. S. McCormick, M. R. Scott, A. M. Stuart. Physica D: Nonlinear Phenomena, 245(1):34-45, 2013. Online publication.
Phase diagrams for knotted and unknotted ring polymers. A. Swetnam, C. Brett, M. P. Allen. Physical Review E, 85(3), 2012. Online publication.