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Article
Publication date: 1 December 1998

A. Bossavit, P. Chaussecourte and B. Métivet

By using complementarity (solving for both potentials, scalar and vector), one often can provide bilateral bounds for some quantities of interest, like for instance the reluctance…

107

Abstract

By using complementarity (solving for both potentials, scalar and vector), one often can provide bilateral bounds for some quantities of interest, like for instance the reluctance of a circuit. However, the vector potential method is expensive, and does not make use of information acquired in the first phase of solving for the scalar potetential. We show how to improve on this by a “local correction” process which, starting from h = grad φ, yields a divergence‐free b, close to μh, by a series of local and independent (parallel) problems.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 17 no. 6
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 March 1992

J. FRÖHLICH and R. PEYRET

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a…

191

Abstract

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

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International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 29 August 2019

Yongshuai Wang, Md. Abdullah Al Mahbub and Haibiao Zheng

This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems.

96

Abstract

Purpose

This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems.

Design/methodology/approach

To avoid difficulty caused by the trilinear term, the authors use the characteristic method to deal with the time derivative term and the advection term. The space discretization adopts the low-order triples (i.e. P1-P1-P1 and P1-P0-P1 triples). As low-order triples do not satisfy inf-sup condition, the authors use the stability technique to overcome this flaw.

Findings

The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates.

Originality/value

Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.

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International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 August 2001

Jaroslav Mackerle

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the…

1686

Abstract

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Details

Engineering Computations, vol. 18 no. 5/6
Type: Research Article
ISSN: 0264-4401

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