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$$\varphi -$$FD: A Well-conditioned Finite Difference Method Inspired by $$\varphi -$$FEM for General Geometries on Elliptic PDEs
Michel Duprez, Vanessa Lleras, Alexei Lozinski, Vincent Vigon and Killian Vuillemot Journal of Scientific Computing 104(1) (2025) https://doi.org/10.1007/s10915-025-02914-0
Low-order fictitious domain method with enhanced mass conservation for an interface stokes problem
Daniele C. Corti, Guillaume Delay, Miguel A. Fernández, Fabien Vergnet and Marina Vidrascu ESAIM: Mathematical Modelling and Numerical Analysis 58(1) 303 (2024) https://doi.org/10.1051/m2an/2023103
A penalty-free Shifted Boundary Method of arbitrary order
J. Haydel Collins, Alexei Lozinski and Guglielmo Scovazzi Computer Methods in Applied Mechanics and Engineering 417 116301 (2023) https://doi.org/10.1016/j.cma.2023.116301
ϕ-FEM for the heat equation: optimal convergence on unfitted meshes in space
Michel Duprez, Vanessa Lleras, Alexei Lozinski and Killian Vuillemot Comptes Rendus. Mathématique 361(G11) 1699 (2023) https://doi.org/10.5802/crmath.497