Seminar: On Space-Time Finite Element Methods for the Optimal Control of Advection-Diffusion Systems

Time:

Venue/Location: Phòng C102, VIASM

Báo cáo viên:Tạ Thị Thanh Mai (Hanoi University of Science and Technology)

Tóm tắt: In this talk, I will present a rigorous numerical analysis of a space-time discretization for distributed optimal control problems governed by advection-diffusion equations under energy regularization. I characterize the first-order optimality conditions as a coupled variational system and establish its equivalence to the original control problem. Utilizing fully unstructured space-time simplicial meshes, we develop a Petrov-Galerkin finite element framework and prove its well-posedness by verifying a discrete inf-sup stability condition. Under suitable regularity assumptions on the state and adjoint variables, I derive a priori error estimates that are optimal with respect to the associated discrete norm. Finally, numerical experiments are presented to validate the theoretical convergence rates and demonstrate the robustness of the scheme across various advective and diffusive regimes.