Consider the differential equation where a, b, c, and f are known functions of position x. (a) Develop the weak form over a typical element Ωe = (xa, xb) such that the bilinear form is symmetric, (b)...

Consider the differential equation

where a, b, c, and f are known functions of position x. (a) Develop the weak form over a typical element Ωe = (xa, xb) such that the bilinear form is symmetric, (b) identify the bilinear and linear forms and construct the quadratic functional, (c) discuss the type of finite element approximation of u that may be used, and (d) develop the finite element model of the equation.