Connecting random fields on manifolds and stochastic partial differential equations in simulations
Journal article, 2023

Modern discretization and solution methods for time-dependent PDEs consider the full problem in space and time simultaneously and aim to overcome limitations of classical approaches by first discretizing in space and then solving the resulting ODE, or first discretizing in time and then solving the PDE in space.

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 1 349-352

Stochastic 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

More information

Latest update

11/20/2024