# 2D formulation for Electrostatic Problems

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(→2D formulation for Triangular Elements) |
(→Stiffness Matrix K<sup>(e)</sup>) |
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::<math>\mathbf{B^T} \mathbf{\varepsilon} \mathbf{B} = | ::<math>\mathbf{B^T} \mathbf{\varepsilon} \mathbf{B} = | ||

− | + | \frac{1}{|\mathbf{J^{(e)}}|^2} | |

\begin{bmatrix} | \begin{bmatrix} | ||

\displaystyle \frac{\partial N_1}{\partial \alpha} & | \displaystyle \frac{\partial N_1}{\partial \alpha} & |

## Revision as of 17:20, 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)}