# 2D formulation for Electrostatic Problems

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− | \int_{\Omega^{(e)}} \mathbf{N^T} \rho_S \partial \Omega^{(e)} | + | \int_{\Omega^{(e)}} \mathbf{N^T} \rho_S \partial \Omega^{(e)} = |

\int \int_{A^{(e)}} \mathbf{N^T} \rho_S d x d y = | \int \int_{A^{(e)}} \mathbf{N^T} \rho_S d x d y = | ||

\int_0^1 \int_0^{1-\beta} |\mathbf{J^{(e)}}| \mathbf{N^T} \rho_S d \alpha d \beta = | \int_0^1 \int_0^{1-\beta} |\mathbf{J^{(e)}}| \mathbf{N^T} \rho_S d \alpha d \beta = |

## Revision as of 19:17, 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)}

### Source Vector f^{(e)}