User:Eml5526.sp11.team1.adam/HW4

=Homework Problem 4.2: Weak form for the equation of heat conduction= Fish and Belystschko page73, Problem 3.5.

Obtain the weak from for the equation of heat conduction with the boundary conditions $$ T\left(0\right) = 100$$ and $$ q\left(10\right) = h\bar{T} $$. The condition on the right is a convection condition.

Multiplying by the weight function
Multiplying the first two equations by the weight funtion we can write:

Applying integration by parts
Applying integration by parts to $$\left(4.2.2a\right)$$ we ca write:

Therefore we can write that:

Using the natural boundary condition we can write:

Which yields

Weak form for 1D heat conduction problems
Therefore the weak form for 1D heat conduction problems can be written as follows: