A Survey of Software for Partial Differential Equations

Machura, Marek; Sweet, Roland A.

doi:10.1145/355921.355922

Cited by 35 publications

(6 citation statements)

References 34 publications

(32 reference statements)

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“…If a survey is made of general purpose _Ivers for differential systems (Machura and Sweet, 1980), it is seen that despite the emergence of many new methods for the solution of such systems, _he method of choice continues to be the method of lines. It has been used in a variety of codes.…”

Section: Mathematical Model 121 Go'_erning Equationsmentioning

confidence: 99%

Colloid transport code-nuclear user`s manual

Jain¹

1992

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Section: Mathematical Model 121 Go'_erning Equationsmentioning

confidence: 99%

Colloid transport code-nuclear user`s manual

Jain¹

1992

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“…The model equations are solved using the method of lines. Since the model comprises a system of coupled parabolic partial differential equations, the method of lines is ideally suited (Machura and Sweet, 1980;Sincovec and Madsen, 1975) for this purpose. With this approach, the space variables are first discretized (in this case, using second-order accurate central differences), and the resulting system of ordinary differential equations (ODEs) is solved by an appropriate ODE solver.…”

Section: Methods Of Solutionmentioning

confidence: 99%

Dynamic nonisothermal transport in hygroscopic porous media: Moisture diffusion in wood

Avramidis¹,

Englezos²,

Papathanasiou³

1992

AIChE Journal

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A model that predicts heat and moisture transfer in the hygroscopic range of a complex porous material such as wood, was evaluated with unsteady-state nonisothermal diffusion experimental data. Water chemical potential gradient was taken as the driving force for diffusion, and the derivation of the temperature-gradient phenomenological coefficient in the mass balance equation was based on the principles of nonequilibrium thermodynamics. The results reveal an excellent prediction of the specimen's average moisture content during desorption in the hygroscopic range. Moreover, a very good agreement was also shown between the specimen's center temperature and the model predictions. The model revealed the existence of a thermal-diffusion phenomenon during the initial stages of the desorption process. This phenomenon was not predicted by Fick's equation for diffusion.

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“…Many of the standard user-oriented features and logical switches employed in these four stages were borrowed from existing software, much of which was surveyed in [16]. FEMOL 1 has the capabilities to solve coupled systems of linear and nonlinear parabolic PDEs with piecewise linear elements in one space dimension, with smooth or unsmooth initial data, and general separated end-point boundary conditions.…”

Section: Computational Procedures and Examplesmentioning

confidence: 99%

“…survey in [16]) generally have no facility to estimate and control both components of the error. In this approach a problem is first discretized in space, for example, by a Galerkin or difference method.…”

Section: Introductionmentioning

confidence: 99%

The finite element method for parabolic equations

Bieterman

Babuška

1982

Numer. Math.

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In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectiveness of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straightforwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems.

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A Survey of Software for Partial Differential Equations

Cited by 35 publications

References 34 publications

Colloid transport code-nuclear user`s manual

Colloid transport code-nuclear user`s manual

Dynamic nonisothermal transport in hygroscopic porous media: Moisture diffusion in wood

The finite element method for parabolic equations

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