Mihai Nechita
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

Numerical analysis for partial differential equations (PDEs) traditionally considers problems that are well-posed in the continuum. However, when a part of the boundary is inaccessible for measurements or no information is given on the boundary at all, the problem might be ill-posed and solving it requires regularization. In this talk, we consider fluid-structure interaction (FSI) models for which noisy velocity measurements in a subset of the computational domain are given. We present a stabilized finite element method (FEM) for this ill-posed unique continuation/data assimilation problem, based on PDE-constrained optimisation with discrete regularisation. Such a stabilized FEM for ill-posed FSI problems can be used in applications related to blood flow and medical imagining data, e.g. 4d-flow MRI data measuring the 3d velocity field of a tissue. We will illustrate such applications with numerical examples.