Finite Element Method Assignment

The goal of this assignment is to use the FEM to solve the same problem we solve in Assignment II (coaxial transmission line problem). To answer the theory questions of this assignment, study Section 6.3 of the textbook.

The assignment is divided into three main parts:

1. State and give a brief description of the basic steps for solving the Poisson Equation using the FEM.
2. What are the element and the assembly matrices? What is the relation between the element and assembly matrices?
3. Download the finite element codes and mesh FEMpoisson.m, CmpElMtx.m and unimesh0.mat. 
   1. What is the sparsity of the assembly matrix A? Write a sparse matrix implementation of A in FEMpoisson.m. 
   2. Use the Matlab profiler to measure the performance of FEMpoisson.m. What is the part of the code where most of the time is spent? Compare the performance of the full and sparse implementations of FEMpoisson.m.
   3. Plot the Potential.
      1. Hint: check Textbook Section 6.5.6 how to plot the FEM grid and values.
   4. Measure the error of the FEM code using the capacitance result: you can take the finite difference high-resolution capacitance result and compare it with the FEM capacitance result.
      1. What is the Finite-Difference resolution that gives an error that is comparable to the FEM error?
   5. How would the FEM governing equations and solution change if we used symmetry BCs and solved Poisson equation only in 1/4 of the domain as we did in the Finite-Difference case?