Spectral element method

Summary

The spectral element method is a finite element method that uses high-degree polynomials on a few large elements. Its nodes and quadrature come from a spectral method. On each element, usually a quadrilateral or hexahedron, the basis consists of Lagrange polynomials at the Gauss–Lobatto–Legendre points. It combines the geometric flexibility of finite elements with the fast convergence of spectral methods for smooth solutions. It was introduced by Anthony Patera for fluid dynamics, and is widely used in seismology and in simulations of turbulent flow. See the definition.