Qiwei Feng

activity

20242026

collaborators

8 papers

math.NA2026

Efficient and simple fourth-order compact finite difference methods for convection-diffusion-reaction equations on arbitrary curved domains

Qiwei Feng, Bin Han, Peter Minev

In this paper, we discuss the 2D convection-diffusion-reaction equation with variable smooth coefficients and the Dirichlet boundary condition on a complicated, thin, and curved do…

math.NA2026

Fourth-order compact finite difference methods for 2D and 3D nonlinear convection-diffusion-reaction equations

Qiwei Feng

In this paper, we first consider linear 2D and 3D convection-diffusion-reaction equations $- \nabla \cdot (κ \nabla u) + v \cdot \nabla u + λ u = ϕ$ and $u_t - \nabla\cdot (κ\nab…

math.NA2025

Convergent Compact Finite Difference Methods with Symmetric Matrices and Highest Possible Orders for Variable-Coefficient Elliptic Equations

Qiwei Feng, Bin Han, Michelle Michelle +1

For the $d$ -dimensional variable-coefficient Poisson problem $- \nabla \cdot (a \nabla u) = f$ subject to Dirichlet boundary conditions, we seek compact (i.e., $3^{d}$ -point) symmetric fi…

math.NA2025

Fourth-Order Compact FDMs for Steady and Time-Dependent Nonlinear Convection-Diffusion Equations

Qiwei Feng, Catalin Trenchea

In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonline…

math.NA2025

A High-Order, Pressure-Robust, and Decoupled Finite Difference Method for the Stokes Problem

Qiwei Feng, Bin Han, Michael Neilan

In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $ν$ in an axis-aligned domain $Ω$ . We decouple the velocity $\…

math.NA2025

The convergence proof of the sixth-order compact 9-point FDM for the 2D transport problem

Qiwei Feng

It is widely acknowledged that the convergence proof of the error in the $l_{\infty}$ norm of the high-order finite difference method (FDM) and finite element method (FEM) in 2D is…

math.NA2024

A Derivative-Orthogonal Wavelet Multiscale Method for 1D Elliptic Equations with Rough Diffusion Coefficients

Qiwei Feng, Bin Han

In this paper, we investigate 1D elliptic equations $- \nabla \cdot (a \nabla u) = f$ with rough diffusion coefficients $a$ that satisfy $0 < a_{m i n} \leq a \leq a_{m a x} < \infty$ and $f\in L…

math.NA2024

Distinct Numerical Solutions for Elliptic Cross-Interface Problems Using Finite Element and Finite Difference Methods

Qiwei Feng

In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by…