We implement the finite element method to solve a variational problem that is inspired by medical imaging. In our application, the domain of the image does not need to be a rectangle and can contain a cavity in the middle. The standard approach to solve a variational problem involves formulating the problem as a partial differential equation. Instead, we solve the variational problem directly, using only techniques available to anyone familiar with vector calculus. As part of the computation, we also explore how triangulation is a useful tool in the process.
Komperda, Tim and Au-Yeung, Enrico
"Triangulation and finite element method for a variational problem inspired by medical imaging,"
DePaul Discoveries: Vol. 10:
1, Article 16.
Available at: https://via.library.depaul.edu/depaul-disc/vol10/iss1/16