Modeling shallow water waves via CG-FEM with monolithic convex limiting

Modeling shallow water waves via CG-FEM with monolithic convex limiting

Internship Description

In recent years, a large number of methodologies have been proposed to solve hyperbolic conservation laws via continuous Galerkin finite elements. Most of these ideas depend upon limiters that correct the fluxes in order to impose bounds on the solution. These techniques have raised continuous Gelerkin finite elements once again as a valid methodology to solve hyperbolic conservation laws and convection- dominated problems. In this project we concentrate on recently developed methods designed for scalar conservation laws and adapt them to the shallow water equations.​​​​

Deliverables/Expectations

​- Implementation of monolithic convex limiting in an existing finite element code
- Comparison of this technique with existing algorithms​

Faculty Name

David Ketcheson

Field of Study

Applied mathematics and computational science