Achieving Higher-Order Convergence Rates in Numerical Homogenization

Explore the construction of higher-order multiscale methods within the Localized Orthogonal Decomposition approach in this 53-minute talk. Discover how to achieve higher-order estimates in elliptic settings without imposing strict regularity conditions on the domain, coefficient, or exact solution. Examine extensions to time-dependent problems and the necessary adaptations. Gain insights from numerical examples that demonstrate the theoretical findings. Delve into advanced numerical homogenization techniques and their applications in solving complex mathematical problems.