Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains
For researchers in numerical analysis and optimal control, this provides theoretical error bounds for XFEMs in non-convex domains, but the contribution is incremental as it extends existing methods to a specific problem class.
The paper analyzes two XFEMs for optimal control problems governed by Poisson equation in non-convex domains, deriving optimal error estimates for state, co-state, and control, which are confirmed by numerical results.
This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous problems, and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations. Optimal error estimates are derived for the state, co-state and control. Numerical results confirm our theoretical results.