2009
DOI: 10.1002/nme.2748
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Adaptive Kronrod–Patterson integration of non‐linear finite element matrices

Abstract: Efficient simulation of unsaturated moisture flow in porous media is of great importance in many engineering fields. The highly non-linear character of unsaturated flow typically gives sharp moving moisture fronts during wetting and drying of materials with strong local moisture permeability and capacity variations as result. It is shown that such conflict with the common preference for low-order numerical integration in finite-element simulations of unsaturated moisture flow: inaccurate numerical integration … Show more

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Cited by 5 publications
(8 citation statements)
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“…Such link has been observed in earlier publications (Kavetski, Binning, and Sloan 2002;Janssen 2010;Rode and Juhl 2013), but no straightforward explanation is available. It is probably a result of the complex interaction between spatial discretization, temporal discretization, convergence criteria and boundary conditions, all affecting the numerical stability of the iterative procedure.…”
Section: Introductory Observationsmentioning
confidence: 60%
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“…Such link has been observed in earlier publications (Kavetski, Binning, and Sloan 2002;Janssen 2010;Rode and Juhl 2013), but no straightforward explanation is available. It is probably a result of the complex interaction between spatial discretization, temporal discretization, convergence criteria and boundary conditions, all affecting the numerical stability of the iterative procedure.…”
Section: Introductory Observationsmentioning
confidence: 60%
“…Finally, all in all, the efficiency and accuracy estimates for the finite-element and control-volume models agree fairly well: for most cases, the iteration counts and mass errors are quite alike -remember though that our controlvolume model employs integral averaging (Kalagasidis, Bednar, and Hagentoft 2004) combined with adaptive integration (Janssen 2010), an implementation which exceeds common practice. Disagreements are found for driving rain and capillary absorption with control volumes.…”
Section: Introductory Observationsmentioning
confidence: 80%
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