A Relationship With The Spectral Element Method
One can show that if is infinitely differentiable, then the numerical algorithm using Fast Fourier Transforms will converge faster than any polynomial in the grid size h. That is, for any n>0, there is a such that the error is less than for all sufficiently small values of . We say that the spectral method is of order, for every n>0.
Because a spectral element method is a finite element method of very high order, there is a similarity in the convergence properties. However, whereas the spectral method is based on the eigendecomposition of the particular boundary value problem, the spectral element method does not use that information and works for arbitrary elliptic boundary value problems.
Read more about this topic: Spectral Method
Famous quotes containing the words relationship, spectral, element and/or method:
“But the relationship of morality and power is a very subtle one. Because ultimately power without morality is no longer power.”
—James Baldwin (1924–1987)
“How does one kill fear, I wonder? How do you shoot a spectre through the heart, slash off its spectral head, take it by its spectral throat?”
—Joseph Conrad (1857–1924)
“Truly, though our element is time,
We are not suited to the long perspectives
Open at each instant of our lives.”
—Philip Larkin (1922–1986)
“Traditional scientific method has always been at the very best 20-20 hindsight. It’s good for seeing where you’ve been. It’s good for testing the truth of what you think you know, but it can’t tell you where you ought to go.”
—Robert M. Pirsig (b. 1928)