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Explore the Localised Orthogonal Decomposition (LOD) method for solving heterogeneous mixed-dimensional elliptic problems in this 27-minute mathematical conference talk. Learn how this computational approach constructs locally supported basis functions on coarse meshes that adapt to specific problem characteristics, ensuring optimal convergence rates while maintaining exponentially decaying localisation errors. Discover the theoretical foundations behind this method and examine numerical experiments that validate the mathematical findings. Gain insights into current research developments extending this framework to hyperbolic problems, making this presentation valuable for researchers and practitioners working in numerical analysis, partial differential equations, and computational mathematics.
