I am planning to study the finite element method for reaction-diffusion systems as well as numerical analysis using FEM in Matlab.
Google, Google scholar(https://scholar.google.ca/) (not all of them are freely accessible) and for free papers/journals you can try Sci-Hub (https://citationsy.com/blog/download-research-papers-scientific-articles-free-scihub/)
If the time scale of your reaction is small and if it is not small you have two different approaches
1- For not reactive transport (time scale of your reaction is not very fast):
Reaction-Diffusion is handled with operator splitting (reaction part + diffusion part)
For reaction part you only need a ODE solver, something like a Runge Kutta or Huen or Euler method or... you can go to RK4-5 for adaptive time step. Then diffusion part: Any finite element general book is good. decause diffusion, heat equation, stress in elasticity and Darcy flow in ground water, and Maxwell equation in electromagnetic are exactly the same! so Just pick up a Finite element book but make sure it is not written for structure analysis: I suggest the classic book by Reddy:
Introduction to the Finite Element Method by Reddy, J. N.
It has full instructor manual and solved problem, and it is a readable book for a beginner. If you want more on the crux of math of finite element and less application see the classic book by G. Fix and Gilbert Strang:
An Analysis of the Finite Element Method
2- If your reaction(s) are very fast, you cannot do "operator splitting" and you have to solve the system in one shot (fully implicit method) or with iteration between diffusion and reaction operators. The way here is not as easy and paved as the case 1 but look at this very well written Review Book Chapter:
Steefel, C. I., & MacQuarrie, K. T. (1996). Approaches to modeling of reactive transport in porous media. Reviews in Mineralogy and Geochemistry, 34(1), 85-129.
It exactly tells you the way to proceed forward for dealing with fast reactions in trasnport.
I hope this helps you
Chapter 4 in " Numerical Methods and Analysis of Multiscale Problems" by Alexandre L M
I recommend, go through the theory behind FEM first. Get a fundamental book from your library moreover, thousands of lectures can be found online for free. Then move to research papers for applications:
https://www.sciencedirect.com/search?qs=finite%20element%20method%20for%20reaction-diffusion%20systems&show=25&sortBy=relevance
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