I am interested in solving the signed distance equation with Discontinuous Galerkin methods. Solving for \varphi

where

and \phi is a level set function. I found this implementation: https://arxiv.org/pdf/1705.01442.pdf , but it uses finite difference instead of finite element. Is there any resource to help me translate that into DG finite elements? Maybe by using the dolfin_dg library (https://bitbucket.org/nate-sime/dolfin_dg/src/master/) ?