# 2D formulation for Electrostatic Problems

From KratosWiki

The 2D Electrostatic Poisson's equation given by the governing PDE and its boundary conditions:

can be written as (see the General formulation for Electrostatic Problems):

with (* n* is the number of nodes of the element):

## 2D formulation for Triangular Elements

After applying the numerical integration for triangular elements by using the natural coordinates, we obtain:

*x*=*N*_{1}*x*_{1}+*N*_{2}*x*_{2}+*N*_{3}*x*_{3}= (1 − α − β)*x*_{1}+ α*x*_{2}+ β*x*_{3}

*y*=*N*_{1}*y*_{1}+*N*_{2}*y*_{2}+*N*_{3}*y*_{3}= (1 − α − β)*y*_{1}+ α*y*_{2}+ β*y*_{3}

### Stiffness Matrix K^{(e)}