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| Assignment 4: |
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Solve 1, and one of 2, 3, or 4. Or more for extra credit.
- Use ACF and implement your own routine (you can use interp2d.m
and tri_quadcofs.m) that computes the error on a triangular grid.
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Confirm the expected order of convergence of linear FE in
L2 and H1 norms for Poisson's equation
on unit square, where the true solution is u(x,y)=sin(pi*x)*sin(pi*y).
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Confirm that the same order can be obtained if you used instead the
Neumann condition on the top boundary (what is the data for this
problem?).
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Confirm that the order is the same when u(x,y)=1+exp(x+y). (For
this problem you need to define appropriate boundary and load data).
- Outline i) the theory and ii) FE algorithm
to solve a stationary diffusion problem for which the coefficient K(x,y)=1+exp(x+y).
In particular, i) what are the coercivity and continuity constants ? ii) How
do you need to modify the code in stima3.m ?
- Similar to 2, but with K(x,y)=1 except inside a circle
located in the center of the unit square, where
K(x,y)=10^a. (Consider $a=1,2,3$).
- Extra: you can implement problems 2 and 3 above. Use homogeneous
load function and homogeneous flux conditions on top and bottom, and a
linear boundary condition u(x,y)=x on the left and right boundaries.
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