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  "body": "\n## Summary\n\nA discontinuous Galerkin method is a [[Galerkin method|Y5B0PEBKE8]] whose trial and test functions are polynomials on each element of a mesh.\nNo continuity is required between elements.\nElements are coupled only through numerical fluxes on their common faces, as in a [[finite volume method|HGKN8E09RS]].\nIt combines the high order of [[finite element methods|98GZ9DVHTA]] with the local conservation and upwinding of finite volume schemes.\nIt was introduced by Reed and Hill for the neutron transport equation, and is widely used for [[conservation laws|8RA7AMWSAF]].\nSee the [[definition|J332CQ8SPB]].\n\n## Explanations\n\n### L1 human\n\nCut the domain into pieces and, on each piece, approximate the solution by its own polynomial.\nThe polynomials of neighbouring pieces need not agree at the boundary, so the approximation may jump there.\nThe pieces talk to each other only through a flux at their common boundary, chosen so that what leaves one piece enters the next.\nWith polynomials of degree zero, each piece holds one number, and the method is a finite volume scheme.\n",
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