A combined spectral-finite element method for solving two-dimensional unsteady Navier-Stokes equations
type: Item
instance of: scholarly article
title: A combined spectral-finite element method for solving two-dimensional unsteady Navier-Stokes equations
zbMATH Open document ID: 0758.76032
DOI: 10.1016/0021-9991(92)90015-Q
author: Weiming Cao
author: Ben-Yu Guo
published in: Journal of Computational Physics
publication date: 1993-01-17T00:00:00Z
review text: In the paper a spectral finite element approach for solving two dimensional, semi-periodic unsteady Navier-Stokes equations is generalized. Previous methods which are mentioned in the introduction, i.e. the finite difference method or combined Fourier-Chebyshev approximation, cannot easily be extended to three dimensional problems with non rectangular domains. The advantage of the method proposed is that it can be generalized easily to more complicated problems. The solution scheme for the combined spectral FEM is constructed. The resulting equation is approximated directly while the incompressibility condition first is softened by the artificial compression term. It leads in fact to the penalty method. The penalty function is calculated with reduced integration to increase the convergence. The convergence theorem is given and proved. Numerical results exhibit lower error in the case of the proposed method compared to the finite element method. The paper is written concisely and may be interesting for researchers as well as those who wish to develop numerical tools of calculations.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 97172
zbMATH Keywords: artificial compression term
zbMATH Keywords: penalty method
reviewed by: C. I. Bajer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 97172