The spectral element method is a high-order finite element technique that combines the geometric flexibility of finite elements with the high accuracy of spectral methods. Six pairs of vortices are observed, as shown by isosurfaces of time-mean swirl velocity. Spectral element outlines are shown in black. The experimental results were obtained by Lachlan Graham. Pressure and streamwise vorticity contours from a spectral element direct numerical simulation of flow past a stationary circular at a Reynolds number of 265, illustrating Mode B shedding.
Coloured contours are of temperature, streamlines are white, spectral element boundaries are black.
For smooth function spaces it can be shown that the resulting interpolants converge exponentially fast as the order of the interpolant is increased. Gauss-Lobatto quadrature delivers diagonal mass matrices. Static condensation Direct matrix solutions are sped up by using static condensation coupled with bandwidth reduction algorithms to reduce storage requirements for assembled system matrices. While the numerical method is very accurate and efficient, it also has the advantage that complex geometries can be accommodated by employing unstructured meshes. Exterior boundaries of spectral elements can be produced using finite-element mesh generation procedures.