An interface-unfitted finite element method for elliptic interface optimal control problem
It provides a numerical method for solving optimal control problems with interfaces, which is relevant for applications in materials science and fluid dynamics, but the approach is an extension of existing methods.
This paper develops and analyzes an interface-unfitted finite element method for linear-quadratic optimal control problems governed by elliptic interface equations, deriving optimal error estimates and verifying them numerically.
This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an interface-unfitted finite element method due to [A. Hansbo and P. Hansbo. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg., 191(47-48): 5537-5552, 2002] to discretize corresponding state and adjoint equations, where piecewise cut basis functions around interface are enriched into standard conforming finite element space. Optimal error estimates in both $L^2$ norm and a mesh-dependent norm are derived for optimal state, co-state and control under different regularity assumptions. Numerical results verify the theoretical results.