multigrid Dupuis & Chopard code

I am trying to create a code for multigrid refinement based on Dupuis & Chopard equations but I dont know how to begin creating this code. Mainly, it is about coarse grid and fine grid mesh. I dont know how to put those to different mesh in one channel. any help will be appretiated.

[Image Analyst]

There are a lot of equations named after a lot of people and I don't know how many people know your two. So you might want to read this: http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer and supply more background, such as equations, code, diagrams, figures, pictures, images, or whatever you have that might help people help you.