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Solving a Bernoulli type free boundary problem with random diffusion
Rahel Brügger, Roberto Croce and Helmut Harbrecht ESAIM: Control, Optimisation and Calculus of Variations 26 56 (2020) https://doi.org/10.1051/cocv/2019030
An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data
A cut finite element method for the Bernoulli free boundary value problem
Erik Burman, Daniel Elfverson, Peter Hansbo, Mats G. Larson and Karl Larsson Computer Methods in Applied Mechanics and Engineering 317 598 (2017) https://doi.org/10.1016/j.cma.2016.12.021
Numerical Mathematics and Advanced Applications - ENUMATH 2013
P. F. Antonietti, Nadia Bigoni and Marco Verani Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications - ENUMATH 2013 103 125 (2015) https://doi.org/10.1007/978-3-319-10705-9_12
The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach
Mimetic finite differences for nonlinear and control problems
P. F. Antonietti, L. Beirão da Veiga, N. Bigoni and M. Verani Mathematical Models and Methods in Applied Sciences 24(08) 1457 (2014) https://doi.org/10.1142/S0218202514400016
On Computation of the Shape Hessian of the Cost Functional Without Shape Sensitivity of the State Variable
Helmut Harbrecht and Johannes Tausch International Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 213 (2014) https://doi.org/10.1007/978-3-319-05083-6_14
Improved trial methods for a class of generalized Bernoulli problems
Constrained Optimization and Optimal Control for Partial Differential Equations
Karsten Eppler and Helmut Harbrecht International Series of Numerical Mathematics, Constrained Optimization and Optimal Control for Partial Differential Equations 160 277 (2012) https://doi.org/10.1007/978-3-0348-0133-1_15
Two Adjoint-Based Optimization Approaches for a Free Surface Stokes Flow
Sabine Repke, Nicole Marheineke and René Pinnau SIAM Journal on Applied Mathematics 71(6) 2168 (2011) https://doi.org/10.1137/100797953
Tracking Neumann Data for Stationary Free Boundary Problems