2. The Basics#
We learn the basic concepts to program in NGSolve, we start with an easy example and we explore the single steps to solve a PDE problem. Then we apply the same steps and concepts to a more complex problem.
basic topics
apply what we have learned Modelling a capacitor in 2D.
2.1. Finite Element Method in a Nutshell#
Problem: (Strong)
Let
Find
With
Multiply the equation by a test function
Problem: (Weak)
Find
Let
Problem: (Discrete-Weak)
Find
Applying the Galerkin method:
Suppose that on the triangulation
Then, by substituting
Then the problem reduces to solve the linear system