Comments for HW3 Part 2
1.a
The error of the energy norm for a 2 element linear Lagrange FEM versus the exact solution is
0.0002282177323.
1.b
The error of the energy norm for a 1 element quadratic Lagrange FEM versus the exact solution
is 0.00003651483716. The single element model was more accurate than the 2-element linear
model though both were fairly accurate.
2.a
The error of the energy norm for a 2 element linear Lagrange FEM versus the exact solution is
0.0002282177323
2.b
The error of the energy norm for a 1 element quadratic Lagrange FEM versus the exact solution
is
. The single P2 element is more accurate than the 2-P1 element model.
3
A function, k1 is introduced to simulate the piecewise function k over the interval [0,1]
3.a
As the number of elements increase, the error is reduced. Also, the change in the error is
smaller with increasing element size suggesting convergence. By inspection, the approximations are
closer to the exact solution as the amount of elements increase.
3.b
The energy norm of the error for a 2-P2 element model is 0.000008051422624. This is
significantly more accurate than a 4-P1 element model. Like the P1 approximations, a table is made to
show the convergence. The accuracy achieved with a 8-P2 element model is about the same as the
accuracy obtained with a 16 to 32 P1 element model.