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Adaptive isogeometric finite element analysis of steady-state groundwater flow

Bekele, Yared Worku; Kvamsdal, Trond; Kvarving, Arne Morten; Nordal, Steinar
Journal article, Peer reviewed
Accepted version
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Bekele2015aif-PostPrint.pdf (3.389Mb)
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http://hdl.handle.net/11250/2479109
Utgivelsesdato
2015
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  • Institutt for bygg- og miljøteknikk [2849]
  • Institutt for matematiske fag [1432]
  • Publikasjoner fra CRIStin - NTNU [20842]
Originalversjon
International journal for numerical and analytical methods in geomechanics (Print). 2015, 40 738-765.   10.1002/nag.2425
Sammendrag
Numerical challenges occur in the simulation of groundwater flow problems because of complex boundary conditions, varying material properties, presence of sources or sinks in the flow domain, or a combination of these. In this paper, we apply adaptive isogeometric finite element analysis using locally refined (LR) B-splines to address these types of problems. The fundamentals behind isogeometric analysis and LR B-splines are briefly presented. Galerkin's method is applied to the standard weak formulation of the governing equation to derive the linear system of equations. A posteriori error estimates are calculated to identify which B-splines should be locally refined. The error estimates are calculated based on recovery of the L2-projected solution. The adaptive analysis method is first illustrated by performing simulation of benchmark problems with analytical solutions. Numerical applications to two-dimensional groundwater flow problems are then presented. The problems studied are flow around an impervious corner, flow around a cutoff wall, and flow in a heterogeneous medium. The convergence rates obtained with adaptive analysis using local refinement were, in general, observed to be of optimal order in contrast to simulations with uniform refinement.
Utgiver
Wiley
Tidsskrift
International journal for numerical and analytical methods in geomechanics (Print)

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