This Python module approximates the optimal control of the Poisson equation written in displacement-pressure (or temperature-heat flux) formulation:
min (1/2){alpha |u - ud|^2 + beta |p - pd|^2 + gamma |q|^2}
subject to p + nabla u = 0, in Omega,
div p = - q, in Omega,
u = 0, on Gamma,
over all controls q in L^2(Omega).
Here, u and p are the displacement and pressure (or temperature and heat flux, respectively). Mixed and Hybrid finite element methods using the lowest order Raviart-Thomas finite elements are utilized. The computational domain is the unit square (0, 1)^2.
Performance with the usual H1-conforming FEM was compared based on an eigenfunction of the Dirichlet Laplacian.
For more details, refer to the manuscript: G. Peralta, Error Estimates for Mixed and Hybrid FEM for Elliptic Optimal Control Problems with Penalizations, preprint.
Gilbert Peralta Department of Mathematics and Computer Science University of the Philippines Baguio Governor Pack Road, Baguio, Philippines 2600 Email: grperalta@up.edu.ph