## UC Berkeley / Lawrence Berkeley Laboratory

#### Jet Schemes and Gradient-Augmented Level Set Methods

**Benni Seibold, Temple University**

##### April 10th, 2013 at 4PM–5PM in 939 Evans Hall [Map]

Jet schemes are semi-Lagrangian advection approaches that evolve parts of the
jet of the solution (*i.e.*, function values and higher derivatives) along
characteristic curves. Suitable Hermite interpolations give rise to methods
that are high order accurate, yet optimally local, *i.e.*, the update for the
data at any grid point uses information from a single grid cell only. Jet
schemes can be systematically derived from an evolve-and-project methodology in
function spaces, which in particular yields stability estimates. We present a
comparison of the accuracy and computational cost of jet schemes with WENO and
Discontinuous Galerkin schemes.

For interface evolution problems, jet schemes give rise to gradient-augmented
level set methods (GALSM). These possess sub-grid resolution and yield accurate
curvature approximations. We demonstrate how the optimal locality of jet
schemes gives rise to a straightforward combination with adaptive mesh
refinement (AMR), and provide an outlook on jet schemes for nonlinear
Hamilton–Jacobi equations.