The ADRSolver is designed to solve partial differential equations of the form:

| (6.1) |

in either discontinuous or continuous projections of the solution field. For a full list of the equations which are supported, and the capabilities of each equation, see the table below.

Equation to solve | EquationType | Dimensions | Projections |

∇^{2}u = 0 | `Laplace` | All | Continuous/Discontinuous |

∇^{2}u = f | `Poisson` | All | Continuous/Discontinuous |

∇^{2}u + λu = f | `Helmholtz` | All | Continuous/Discontinuous |

ϵ∇^{2}u + V∇u = f | `SteadyAdvectionDiffusion` | 2D only | Continuous/Discontinuous |

ϵ∇^{2}u + λu = f | `SteadyDiffusionReaction` | 2D only | Continuous/Discontinuous |

ϵ∇^{2}uV∇u + λu = f | `SteadyAdvectionDiffusionReaction` | 2D only | Continuous/Discontinuous |

+ V∇u = f | `UnsteadyAdvection` | All | Continuous/Discontinuous |

= ϵ∇^{2}u | `UnsteadyDiffusion` | All | Continuous/Discontinuous |

+ V∇u = ϵ∇^{2}u | `UnsteadyAdvectionDiffusion` | All | Continuous/Discontinuous |

+ u∇u = 0 | `UnsteadyInviscidBurger` | 1D only | Continuous/Discontinuous |