Finite element analysis

Problem 5. Suppose that the differential equation 2u=f(x;y) with specific boundary conditions, is valid on the region as being represented in the figure below FIGURE: The region divided in four elements. The finite element solution in terms of linear basis functions is given by u(x,y)=0,211+43+6,54+85 (i) Determine the equation of the plane which approximate the function on element 2. Sketch this plane. (ii) Give the approximate solution at (a) node 4 (b) the point (3/4,1/2). (iii) Give the approximate solution of xu at (3/4,1/2) from the finite element solution. (iv) Give an approximation of the flux over 25