Consider a fluid waveguide similar to the Pekeris waveguide, but with a continuously varying sound speed c.z/ in the water column.

a. Using the simple linear elements formulate the FEM equations for the depth-separated wave equation. You may assume the sound speed to be linear (but not constant) within each element.

b. Discuss the factors affecting the choice of element size for this problem.

c. Implement the formulation and perform a numerical convergence analysis for the isovelocity Pekeris waveguide. Compare your results to the analytical solution (e.g., by solving (2.182)).