Discontinuous Galerkin Methods & DGSEM
High-order spectral element and discontinuous Galerkin methods.
This section dives into Discontinuous Galerkin (DG) and Discontinuous Galerkin Spectral Element Methods (DGSEM). These methods combine the local conservation properties of finite volume methods with the high-order accuracy of finite element methods.
Examples
1-D Linear Convection with DG0
An introduction to Discontinuous Galerkin using piecewise-constant (DG0) elements.
1-D Linear Convection with DG1
Extending DG to linear polynomial approximations with a modal basis and SSP RK3.
Starting Points & Planned Examples
- Weak and strong DG forms
- Numerical fluxes (Lax-Friedrichs, Roe, etc.)
- Nodal vs modal bases and quadrature
- 1D DG advection experiments
- Conservation and stability tests