Object-Oriented Field Recovery and Error Estimation in Finite Element Methods

Okstad, Knut Morten; Kvamsdal, Trond

doi:10.1007/978-3-642-57172-5_9

Cited by 1 publication

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“…Then, goal‐oriented recovery of stresses in elasticity and surface forces (drag and lift) for Stokes problems were developed and presented in the papers , and , respectively. Object‐oriented implementation of the SPR recovery procedures is described in and . Recently, we have developed a posteriori error estimates for IGA (see and ).…”

Section: Introductionmentioning

confidence: 99%

Adaptive isogeometric finite element analysis of steady‐state groundwater flow

Bekele

Kvamsdal

Kvarving

et al. 2015

Num Anal Meth Geomechanics

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SUMMARYNumerical challenges occur in the simulation of groundwater flow problems due to 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) Bsplines to address these types of problems. The fundamentals behind isogeometric analysis and LR Bsplines 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.

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