  We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational
principles for waves in lossy media to formulate a finite element method for
solving the complex Helmholtz equation that is based entirely on minimization.
In particular, this method results in a finite element matrix that is symmetric
positive-definite and therefore simple iterative descent methods and
preconditioning can be used to solve the resulting system of equations. We also
derive an error bound for the method and illustrate the method with numerical
experiments.

Numerical Analysis