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advection-diffusion 1asymptotic stability 1cartesian grid method 1critical regularity 1elastic membrane 1finite difference 1global well-posedness 1moving domains 1peskin problem 1robin boundary conditions 1stokes flow 1

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math.NA2026

A Cartesian Grid Method for Advection-Diffusion Equations with Robin Boundary Conditions on Moving Domains

Han Zhou, Yoichiro Mori, Lingxing Yao

The paper presents a Cartesian grid finite‑difference method for solving advection‑diffusion equations with Robin boundary conditions on domains that move over time, using an inter…