1. A brief description of the steps involved in the mathematical formulation of the finite element method for this particular prob

1. A brief description of the steps involved in the mathematical formulation of the finite element method for this particular problem.

The aim of this assignment is to develop a computer program, in Matlab, for the finite element solution of the equation,     0                        u c y u K x y u K x x y using linear triangular finite elements. In the above equation, u is a scalar, Kx and Ky are material parameters (constant within each finite element), λ is a constant and c is a (constant) body force term. The boundary conditions of the problem are given in terms of prescribed values of the function u or zero flux. The assignment will be carried out in groups of no more than three students.

A final report should be submitted by each group, containing the following items:

1. A brief description of the steps involved in the mathematical formulation of the finite element method for this particular problem.

2. A listing of the computer code with a brief description of each relevant part.

3. The solutions to a number of simple problems which demonstrate that the different options available in the code are all working. At least three problems are required, as follows:  One problem with λ = c = 0.  One problem with λ = 0, c ≠ 0.  One problem with λ ≠ 0, c = 0. The problems will be tested with Kx = Ky and Kx ≠ Ky , to test the effect of material orthotropy. If no exact solution is available for comparison, the accuracy of the above solutions should be demonstrated by mesh refinement. After submission, an oral examination will be carried out with all members of each group.