New Problem 5.1: Consider the following pair of differential equations:where are the depe...

New Problem 5.1: Consider the following pair of differential equations:

where are the dependent unknowns, a, b, c and f are given functions of

(a) Develop the weak forms of the equations over a typical element and identify the primary and secondary variables of the formulation. Make sure that the bilinear form is symmetric (so that the element coefficient matrix is symmetric).

(b) Develop the finite element model by assuming approximation of the form

Hint: The weight functions used for the two equations are like respectively.

(c) Comment on the type of interpolation functions (i.e., Lagrange type or Hermite type) and the minimum degree of approximation functions that can be used in this problem.