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Adaptive isogeometric finite element analysis of steady‐state groundwater flow
Author(s) -
Bekele Yared W.,
Kvamsdal Trond,
Kvarving Arne M.,
Nordal Steinar
Publication year - 2015
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2425
Subject(s) - isogeometric analysis , finite element method , mathematics , flow (mathematics) , a priori and a posteriori , groundwater flow , galerkin method , boundary value problem , discontinuous galerkin method , boundary (topology) , mathematical optimization , computer science , mathematical analysis , groundwater , geometry , geology , geotechnical engineering , structural engineering , engineering , aquifer , philosophy , epistemology
Summary 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 L 2 ‐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. Copyright © 2015 John Wiley & Sons, Ltd.