Discontinuous Galerkin method

Summary

A discontinuous Galerkin method is a Galerkin method whose trial and test functions are polynomials on each element of a mesh. No continuity is required between elements. Elements are coupled only through numerical fluxes on their common faces, as in a finite volume method. It combines the high order of finite element methods with the local conservation and upwinding of finite volume schemes. It was introduced by Reed and Hill for the neutron transport equation, and is widely used for conservation laws. See the definition.