Mixed finite element methods for nonlinear reaction-diffusion equations with interfaces
Numerical Analysis
2023-04-27 v1 Numerical Analysis
Abstract
We develop mixed finite element methods for nonlinear reaction-diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations. The stability of semidiscrete solutions, existence and the a priori error estimates of fully discrete solutions are proved by fixed point theorem and continuous/discrete Grnwall inequalities. Numerical results illustrating our theoretical analysis are included.
Cite
@article{arxiv.2304.13376,
title = {Mixed finite element methods for nonlinear reaction-diffusion equations with interfaces},
author = {Jeonghun J. Lee and Xinran Jin},
journal= {arXiv preprint arXiv:2304.13376},
year = {2023}
}