# 2D formulation for Electrostatic Problems

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+ | == 2D formulation for Triangular Elements == | ||

+ | === Stiffness Matrix K<sup>(e)</sup> === | ||

+ | |||

+ | ::<math>\int_{\Omega^{(e)}} \mathbf{B^T} \mathbf{\varepsilon} \mathbf{B} \partial \Omega^{(e)}</math> | ||

+ | |||

+ | ::<math>\oint_{\Gamma_{\infty}^{(e)}} \mathbf{N^T} \alpha \mathbf{N} \partial \Gamma_{\infty}^{(e)}</math> | ||

+ | |||

+ | |||

+ | === Source Vector f<sup>(e)</sup> === | ||

+ | |||

+ | ::<math>\int_{\Omega^{(e)}} \mathbf{N^T} \rho_S \partial \Omega^{(e)}</math> | ||

+ | |||

+ | ::<math>\oint_{\Gamma_q^{(e)}} \mathbf{N^T} \bar D_n \partial \Gamma_q^{(e)}</math> | ||

+ | |||

+ | ::<math>\oint_{\Gamma_V^{(e)}} \mathbf{n^T} \mathbf{N^T} \mathbf{q_n} \partial \Gamma_V^{(e)}</math> | ||

## Revision as of 19:09, 11 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

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