Well, it’s been a long time since I last wrote my daily diary. All these days I have been trying to learn finite element methods. These methods are basically used in engineering problems like heat transfer, elasticity, current flow, computer simulations etc,.
I am following a course on coursera for this topic and it’s going pretty rough, as a lot of mathematical terms have been used like finite dimensional pde, boundary condition, Hilbert Spaces etc. I am already feeling like studying in 12th standard again.
Today, I watched 6 videos of week 2 and it gave a pretty clear understanding of what we are doing. I want to share some general points which are important:
- More interest in finding approximate solution than exact one (harder to find).
- Approximate solution can be found by limiting the solution spaces where Hilbert Space comes into play.
- Hilbert Space only constitutes those functions whose solution is square integeral of itself.
- Divide the whole input domain into smaller intervals, find approximate solution at each one, and then integrate everything to find final answer.