Webrelaunch 2020

Leveraging the power of adaptive computational schemes

  • Speaker: Dr. Pascal Heid
  • Place: 1.067
  • Time: 15.5.2024, 13:30
  • Invited by: Prof. Dr. Dorothee Frey


In many areas of natural sciences and engineering, nonlinear partial differential equations (PDEs) are amongst the most prominent and powerful mathematical modelling tools. However, in applications of practical interest, these objects are typically extremely complicated and their solutions are seldom available in analytical terms. Yet, in many cases, iterative linearisation methods allow to generate a sequence of approximations, which potentially converges to a solution of the original problem. In order to cast these iteration procedures into a computational scheme, they need to be discretised within a finite-dimensional framework. An effective numerical algorithm may be obtained by an instantaneous interplay of the iterative linearisation procedure and an (optimally convergent) adaptive discretisation scheme, referred to as iterative linearised Galerkin method. The bigger picture of this approach shall be outlined, and some research results will be provided. Finally, we will discuss the adaptivity concept in the context of physics-informed neural networks for solving PDEs through deep learning.