We propose a monotone finite element method for convection-diffusion equations based on orthogonal subregion collocation, called monotone orthogonal subregion collocation (MOSC) method. The MOSC method ensures that the resulting stiffness matrix is an M-matrix for general two-and three-dimensional Delaunay meshes. The method is further applied to Newton methods for solving nonlinear diffusion equations and the drift-diffusion equations. Numerical experiments show that the MOSC method admits first-order accuracy in the H1-norm and exhibits excellent stability when solving convection-dominated problems. Numerical experiments for a metal-oxide-semiconductor field-effect transistor device show that the method suppresses non-physical oscillations of numerical solutions effectively, and preserves the maximum principle of quasi-Fermi potentials.

Publication:

JOURNAL OF COMPUTATIONAL PHYSICS

http://dx.doi.org/10.1016/j.jcp.2026.115332

Author:

Junyue Cui

SKLMS, NCMIS, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China

School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100049, China

E-mail addresses: cuijunyue25@mails.ucas.ac.cn

Pengcong Mu

Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China

E-mail addresses: mupengcong@lsec.cc.ac.cn (W. Zheng)

Weiying Zheng

SKLMS, NCMIS, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China

School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100049, China

Corresponding author.

E-mail addresses: zwy@lsec.cc.ac.cn