The Whittaker-Henderson graduation is a data smoothing method commonly used in actuarial science for mortality table computation. This method is a finite-dimensional minimization problem, which aims to give a smooth approximation of the crude data. Our goal is to treat the Whittaker-Henderson method as a minimization problem in a Sobolev space. We take advantage of some results in the study of Sobolev spaces to analyze the solution to the graduation problem. Solving the arising minimization problem is equivalent to solving a partial differential equation (PDE). To solve the PDE numerically, we use the finite element method (FEM). We apply this variational approach to the data sets found in the literature. In particular, we test our method to check for patterns in (1) mortality rates for Filipino males, (2) global average temperature anomaly, and (3) monthly eBay share price. We also compare the results with that of the Whittaker-Henderson method.