Title: Analysis of a finite element method for PDEs in evolving domains with topological changes Abstract The talk presents the first rigorous error analysis of an unfitted finite element method for linear parabolic problems posed on time-dependent domains that may undergo topological changes. The domain evolution is assumed to be…
Title: Dynamic Ritz Projection of Finite Element Methods for Fluid-Structure Interaction Abstract Regardless of the development of various finite element methods for fluid-structure interaction (FSI) problems, optimal-order convergence of finite element discretizations of the FSI problems in the L^{\infty}(0, T; L^2)-norm has not been proved due to the incompatibility between…
Title: Mathematical Modeling and Error Estimation for the Thermal Dunking Problem Abstract We consider the so-called Dunking problem often encountered in engineering heat transfer: a passive solid body at uniform initial temperature T_i is suddenly immersed in a fluid environment at temperature T_\infty. The key quantity of interest is the…
Title: Adjoint-Based Calibration of Nonlinear Stochastic Differential Equation Abstract To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain several parameters which have to be chosen carefully…
Title: Global space-time low-complexity numerical methods for the time-dependent Schrödinger equation Abstract The aim of this talk is to present novel global space-time methods for the approximation of the time-dependent Schrödinger equation on low-complexity manifolds. The backbone of the approach is the use of a least-square formulation of the time-dependent…
Title: An immersed boundary method based on the resolution of an optimal control problem Abstract The numerical resolution of partial differential equations in domains with an intricate, a priori unknown or deforming over time geometry, generally induce difficulties related to mesh generation. Indeed, solving such problems requires, classically, the generation…
Title: A primer on physics-informed machine learning Abstract Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. Practitioners often…
Title: A class of parabolic fractional reaction-diffusion systems with control of total mass: Theory and numerics Abstract: In this talk based on [1, 2], we present some new results about global-in-time existence of strong solutions to a class of fractional parabolic reaction–diffusion systems posed in a bounded open subset of…
Title: Energy consistent time discretisation of port-Hamiltonian systems Abstract Various ordinary and partial differential equations arising from physics can be written as port-Hamiltonian systems. Their Hamiltonian function represents an energy that is conserved or dissipated along solutions. Numerical schemes are energy consistent, if the Hamiltonian is preserved or dissipated also…
Title: Curved meshes for a diffusion problem with a surface Laplacian Abstract We study a diffusion problem with boundary conditions that involve a surface Laplacian. We present the numerical analysis of a high-order finite element discretization. A smooth domain is considered for the definition of this boundary operator. The discrtized…