Charles-Edouard Bréhier: Introduction to numerical methods for SPDEs I

Speaker
Charles-Edouard Bréhier, Université de Pau et des Pays de l’Adour

Abstract
The objective of these lectures is to present the fundamentals on the well-posedness and qualitative properties for parabolic semilinear SPDEs, in particular the regularity properties of the solutions. Then, standard discretization schemes for the temporal and spatial approximation will be presented will be presented, with the techniques used to establish strong and weak error estimates. The focus will be on equations with globally Lipschitz coefficients, with a presentation of challenges and solutions for more complex systems. Finally, more advanced topics, such as the design and analysis of structure preserving algorithms will be discussed.