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math.NA2025
A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods
Moritz Hauck, Alexei Lozinski, Roland Maier
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we a…
math.NA2025
Numerical Approaches for non-local Transport-Dominated PDE Models with Applications to Biology
Johan Marguet, Raluca Eftimie, Alexei Lozinski
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and…
math.NA2023
phi-FEM for the heat equation: optimal convergence on unfitted meshes in space
Michel Duprez, Vanessa Lleras, Alexei Lozinski +1
Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh…