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

04/26/2023

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by   Jeonghun J. Lee, et al.

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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.