User:EML5526.S11.Team3.risher/homework5

5.1
From 26-2:

(3) from 9-2:

$$ \frac{\partial}{\partial x} \left[ (2+3x) \frac{\partial u}{\partial x} \right] + 5x = 0 $$, $$ \forall x \in \left[ 0,1 \right] $$, $$ u(1)=4 $$, $$ -\frac{\partial u(x=0)}{\partial x}=6 $$

$$ \Gamma_g = [0] $$, $$ \Gamma_h = [1] $$

Solve the above problem using Weight Function with apppropriate

$$ F_I, I=p, F, e $$,

until convergence of

$$u^h(0.5)$$ to $$O(10^{-6})$$.

See HW4.4 on 21-1

Plot $$ u, u^h $$, convergence (error vs. n)

5.2
From 26-2:

Same as HW 5.1 but using

$$ \Gamma_g = [1] $$, $$ \Gamma_h = [0] $$

5.3
From 29-6:

Similar to HW 5.1, but using LIBF with uniform discretization (equidistant nodes). m = 4, 6, 8

1.) Explain how LIBF are used as CBS

2.) Plot all LIBF used

3.) Use matlab quad, WA, ... to int

4.) Plot $$ u_m^h $$ vs u and $$ u_m^h(0.5) - u(0.5) $$ vs. m

5.4
From 29-6

Similar to HW 5.1, but using LIBF with uniform discretization (equidistant nodes). m = 4, 6, 8

1.) Explain how LIBF are used as CBS

2.) Plot all LIBF used

3.) Use matlab quad, WA, ... to int

4.) Plot $$ u_m^h $$ vs u and $$ u_m^h(0.5) - u(0.5) $$ vs. m

5.5
From 29-7

Continuation of HW 4.7 on Calculix

1.) For the disk problem, extract:

node info: node numbers are coordinates

element info: element numbers and element nodes

2.) Generate 3 meshes of same disk with triangular elements (increase no. of elements)

3.) Install ccx, run examples, write report for "dummies" (explain commands, screenshots...)

5.6
From 30-6:

Quad Lagrangian element basis function

Plot 3 figures similar to those on 30-5 and 30-6

5.7
From 30-6:

Similar to HW 5.1 and HW 5.3, but using Linear Lagrangian element basis function with uniform discretization (equidistant element nodes, nel = 4, 6, 8 ...)

1.) Explain how Linear Lagrangian element basis function are used as CBS

2.) Plot all Lagrangian element basis function used

3.) Use matlab quad, WA, ... to int

4.) Plot $$ u_{nel}^h $$ versus $$ u $$ and $$ u_{nel}^h(0.5)-u(0.5) $$ versus nel

5.8
From 30-7:

Similar to HW 5.2 and HW 5.4, but using Linear Lagrangian element basis function with uniform discretization (equidistant element nodes, nel = 4, 6, 8, ...)

1.) Explain how Linear Lagrangian element basis function are used as CBS

2.) Plot all Lagrangian element basis function used

3.) Use matlab quad, WA, ... to int

4.) Plot $$ u_{nel}^h $$ versus $$ u $$ and $$ u_{nel}^h(0.5)-u(0.5) $$ versus nel