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 Gr${\"o}$nwall inequalities. Numerical results illustrating our theoretical analysis are included.

翻译：针对具有Robin型界面条件的非线性反应扩散方程, 我们发展混合有限元方法. 引入化学物质的速率作为新变量并重新表述控制方程. 通过不动点定理和连续/离散Grönwall不等式证明了半离散解的稳定性、全离散解的存在性及先验误差估计. 文中还给出了数值实验结果以验证理论分析.