A space-time method for a moving-interface inverse problem

Tóm tắt báo cáo

In this talk, we investigate an inverse problem of determining a term on the right-hand side of an advection-diffusion equation with moving subdomains. The problem is regularized by the Tikhonov method. We use a space-time interface-fitted method to discretize both the state and adjoint. The variational approach is employed for discretizing the source. We establish optimal error estimates in two different norms, together with a priori choice for the regularization parameter that ensures the strong convergence of the discrete source to the exact one.