# 2D formulation for Electrostatic Problems

From KratosWiki

(Difference between revisions)

(→2D formulation for Triangular Elements) |
(→2D formulation for Triangular Elements) |
||

Line 162: | Line 162: | ||

− | ::<math>B(\alpha,\beta)=\mathbf{J^{(e)}} B(x,y) \qquad B(x,y)= \mathbf{J^{(e)}^{-1}} B(\alpha,\beta)</math> | + | ::<math>B(\alpha,\beta)=\mathbf{J^{(e)}} B(x,y) \qquad B(x,y)= \mathbf{(J^{(e)})^{-1}} B(\alpha,\beta)</math> |

## Revision as of 16:59, 12 November 2009

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:

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