Connecting random fields on manifolds and stochastic partial differential equations in simulations
Journal article, 2023
The development of space-time methods for hyperbolic and parabolic differential equation is an emerging and rapidly growing field in numerical analysis and scientific computing. At the first Workshop on this topic in 2017 a large variety of interesting and challenging concepts, methods, and research directions have been presented; now we exchange the new developments.
The focus is on the optimal convergence of discretizations and on efficient error control for space-time methods for hyperbolic and parabolic problems, and on solution methods with optimal complexity. This is complemented by applications in the field of time-dependent stochastic PDEs, non-local material laws in space and time, optimization with time-dependent PDE constraints, and multiscale methods for time-dependent PDEs.
Gaussian random fields
spectral approximation
Riemannian manifolds
sphere
surface finite element methods
stochastic wave equation
stochastic partial differential equations
Author
Annika Lang
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Oberwolfach Reports
1660-8933 (ISSN) 1660-8941 (eISSN)
Vol. 19 1 349-352Stochastic Continuous-Depth Neural Networks
Chalmers AI Research Centre (CHAIR), 2020-08-15 -- .
Efficient approximation methods for random fields on manifolds
Swedish Research Council (VR) (2020-04170), 2021-01-01 -- 2024-12-31.
Subject Categories
Mathematics
Computational Mathematics
Probability Theory and Statistics
DOI
10.4171/OWR/2022/6