Advertisement
Published in:
2022 | OriginalPaper | Chapter
Local- Galerkin Schemes in 1D
Authors : Jürgen Steppeler, Jinxi Li
Published in: Mathematics of the Weather
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
This chapter describes Local-Galerkin (L-Galerkin) methods, which are generalizations of the classic Galerkin procedure. L-Galerkin methods are local and therefore more practical on multiprocessing computers. A well-known example is the spectral element (SE) method, but there exist a large number of alternatives, named onom or the third-degree method. onom approximates the fields in order n and the fluxes in order m. All methods described here use piecewise continuous polynomial spaces and therefore are continuous Galerkin (CG) methods. An important consideration with onom and the classic Galerkin methods is the sparseness of the grid, which is alternatively called the serendipity grid which was already used with the classic Galerkin method. This means that not all points of a regular grid are used and this offers a considerable potential saving of computer time.