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…
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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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…
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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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.
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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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…
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.