A high-order discontinuous Galerkin method for level set problems on polygonal meshes

We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. We analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications. •High-order DG schemes for level set equations on polygonal meshes.•New algorithms for velocity reconstruction inside mesh cells from boundary data.•Using Taylor expansion to calculate the normalized solution gradient.