Mixed finite element methods for nonlinear reaction–diffusion equations with interfaces

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2024-06, Vol.443, p.115756, Article 115756
Main Authors: Jin, Xinran, Lee, Jeonghun J.
Format: Article
Language:English
Subjects:
Error analysis
Interface conditions
Mixed finite element methods
Reaction–diffusion equations
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Summary: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 Grönwall inequalities. Numerical results illustrating our theoretical analysis are included.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2024.115756