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  "body": "\n## Summary\n\nThe spectral element method is a [[finite element method|98GZ9DVHTA]] that uses high-degree polynomials on a few large elements.\nIts nodes and quadrature come from a [[spectral method|MYV657YRDW]].\nOn each element, usually a quadrilateral or hexahedron, the basis consists of [[Lagrange polynomials|Y7KSGE97GK]] at the Gauss–Lobatto–Legendre points.\nIt combines the geometric flexibility of finite elements with the fast convergence of spectral methods for smooth solutions.\nIt was introduced by Anthony Patera for fluid dynamics, and is widely used in seismology and in simulations of turbulent flow.\nSee the [[definition|8PQ405CKA3]].\n\n## Explanations\n\n### L1 human\n\nCut the domain into a few blocks, and on each block use a polynomial of high degree, such as degree $8$.\nNeighbouring blocks agree along their common edges, so the whole approximation is continuous.\nThe polynomial on each block is stored by its values at special points that cluster near the block edges.\nUsing the same points for the integrals makes the mass matrix diagonal, which makes time stepping cheap.\n",
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