Qiwei Feng

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20242026

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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…