Problem Statement:

 

1. Present the assembled GWS^h via LHS Q = RHS before modification for Dirichlet data.
2. Present a plot of the four element temperature distribution.
3. Perform a uniform mesh refinement until the left temperature has converged to within .01, reporting both T_L and Enorm.
4. Plot the converged temperature distribution.

 

Solution:

Applying the GalerkinWeak Statement Recipe yields the following:

S_e( [DIFF]_e {Q}_e = {SRC}_e + {BFLX}_e)

Writing this in MatLab terms yields the following:

GWS^h = [LHS] {Q} = [RHS] where [LHS] = [DIFF] and [RHS] = SRC]+ [BFLX]

	0.4005	-0.4005	0	0	0		Q1		8.0599
	-0.4005	0.802	-0.4015	0	0		Q2		5.7292
GWSh =	0	-0.4015	0.804	-0.4025	0		Q3	=	4.5573
	0	0	-0.4025	0.806	-0.4035		Q4		2.6042
	0	0	0	-0.4035	0.4035		Q5		0.4557

 

 

 

 

 

Results:

 

A Convergence Table for the leftmost temperature is shown below (Table 1), indicating the number of elements used in each approximation and its corresponding element length, temperature, convergence, normal error, and change in normal error.

 

 

 

 

 

4 Element Representation

 

 

128 Element Representation