8 papers · 1 filter
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…
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 and $u_t - \nabla\cdot (κ\nab…
Analysis of Compact Symmetric Finite Difference Methods with Highest Possible Orders for Elliptic Equations
Qiwei Feng, Bin Han, Michelle Michelle +1
For the -dimensional variable-coefficient Poisson problem subject to Dirichlet boundary conditions, we seek compact (i.e., -point) symmetric fi…
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…
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 in an axis-aligned domain . We decouple the velocity $\…
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 norm of the high-order finite difference method (FDM) and finite element method (FEM) in 2D is…