Summer School
Computational Mathematics in Gdańsk
03-09 July 2022

Institute of Mathematics of Polish Academy of Sciences & Gdańsk Uniersity of Technology

Annika Lang (Department of Mathematical Sciences, Chalmers and University of Gothenburg, Sweden)

Introduction to SPDEs and their approximation

Abstract: To simulate stochastic partial differential equations (SPDEs), we need to understand the basic theory for SPDEs first. We introduce Wiener processes and the stochastic Itô integral on Hilbert spaces before showing existence and uniqueness of solutions to SPDEs and their regularity. We continue with approximating solutions via Galerkin methods and time stepping and discuss the concept of strong and weak convergence. To allow for computations in practice, we will close the lecture series with approximation methods for the driving Wiener process and basics in Monte Carlo simulations.