# Finite Element Methods

## H S Rai

### GNDEC, Ludhiana (India)

# Linear elliptical Differential equation

## in one dimension

1D Elasticity at steady state 1D Mass diffusion at steady state 1D Heat conduction at steady state

# The differential equation:

- \(\dfrac{d\sigma}{dx} + f(x) = 0\) in \((0, L)\)

# Introduction

- A method to solve Engineering Problems
- A approximate method

# Video 4

The differential equation:

\(\frac{d\sigma}{dx} + f(x) = 0 \quad in \quad (0, L)\)

- Open interval: Domain between \(x=0 \quad \& \quad x=L\), excluding endpoints \(x=0 \quad \& \quad x=L\) themseleves.

- Here boundary conditions either on \(u(x)\) or on \(u_{,x}\) at boundary points.