Convergence in Hölder and Sobolev Norms for Galerkin Approximations of Generalized Whittle-Matern Fields
Offered By: Hausdorff Center for Mathematics via YouTube
Course Description
Overview
Explore a lecture on convergence rates for Galerkin approximations of generalized Whittle-Matern fields in Hölder and Sobolev norms. Delve into the analysis of Gaussian random fields with covariance operators given by negative fractional powers of second-order elliptic differential operators. Examine both spectral Galerkin methods and finite element methods, with a focus on their applicability to non-stationary fields on non-standard domains. Learn about optimal strong convergence rates, error analysis, and key elements of deterministic error proofs. Gain insights into numerical simulations and the practical implications of this research, which is particularly relevant for models involving Gaussian fields with adjustable correlation length and smoothness.
Syllabus
Intro
Question
Some approaches (Part 2)
Sampling 2: dealing with fractional powers
Sampling 2: Finite element Galerkin method
Error analysis
Key elements of the proof-deterministic error
Numerical simulations
Taught by
Hausdorff Center for Mathematics
Related Courses
The Finite Element Method for Problems in PhysicsUniversity of Michigan via Coursera 有限元分析与应用 | Finite Element Method (FEM) Analysis and Applications
Tsinghua University via edX Pratiques du Dimensionnement en Mécanique
Université Paris-Saclay via France Université Numerique High Performance Finite Element Modeling
KTH Royal Institute of Technology via edX High Performance Finite Element Modeling – Part 2
KTH Royal Institute of Technology via edX