Approximation of Navier-Stokes incompressible flow using a spectral element method with a local discretization in spectral space

Abstract

A spectral element technique is examined, which builds upon a local discretization within the spectral space. To approximate a given system of equations the domain is subdivided into nonoverlapping quadrilateral elements, and within each element a discretization is found in the spectral space. The difference is that the test functions are divided into the higher-order polynomials, which have zero boundaries and lower-order polynomials, which are nonzero on one boundary. The method is examined for Navier-Stokes incompressible flow for fluid flow within a driven cavity and for flow over a backstep.

Overlapping Schwarz preconditioners for spectral element methods in nonstandard domains and heterogeneous media

“…These techniques have then found application to problems of mesh generations in finite element methods and more recently in spectral element methods; see e.g. [2][3][4]. These methods are high-order generalizations of standard finite element methods where accuracy is improved by increasing the polynomial degree of the basis functions as well as the number of elements; see e.g.…”

A Spectral Element Method for the Navier--Stokes Equations with Improved Accuracy

“…The spectral element method [28] (p-version of finite element method [2]) for solving fluid dynamics problems has gained some attention [10], [7]. As it is well known, the spectral element method retains the flexibility of the finite element method to deal with nontrivial geometries while keeping the accuracy of spectral methods.…”