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math.NA2025
A Besov-based integration-by-parts method for the incompressible Navier-Stokes equations
Xinyu Cheng, Zhaonan Luo, Sheng Wang
This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish th…
math.NA2024
On semi-implicit schemes for the incompressible Euler equations via the vanishing viscosity limit
Xinyu Cheng, Zhaonan Luo, Sheng Wang
A new type of systematic approach to study the incompressible Euler equations numerically via the vanishing viscosity limit is proposed in this work. We show the new strategy is un…
math.NA2023
Unconditionally stable exponential integrator schemes for the 2D Cahn-Hilliard equation
Xinyu Cheng
Phase field models are gradient flows with their energy naturally dissipating in time. In order to preserve this property, many numerical schemes have been well-studied. In this pa…