5 papers
Deep Truncated FBSDE Method for High-Dimensional Nonlinear PDEs and Fully Coupled FBSDEs
Xinyu Cheng, Yunzhang Li, Weiran Xiong
In this paper, we introduce a deep truncated forward-backward stochastic differential equation (FBSDE) method for high-dimensional partial differential equations (PDEs) and fully c…
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…
Global well-posedness and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model
Xinyu Cheng, Zhaonan Luo, Zhaojie Yang +1
In this paper, we consider global strong solutions and the uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model in , where and . The well-recogni…
Viscosity-uniform error estimates for a semi-implicit Fourier method in Besov spaces
Xinyu Cheng, Zhaonan Luo, Sheng Wang
We prove error estimates for a semi-implicit Fourier--Galerkin method for two-dimensional incompressible flow on the torus, with viscosity . The temporal error is first…
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…