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Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

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Nội dung chi tiết: Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysisapplied mechanics and engineeringwww.clscvicr.com/locatc/cniaSuperconvergent patch recovery and a posteriori error estimation technique in adaptive is

ogeometric analysisMukcsh Kumar* *-1. Trond Kvamsdal, Kjctil Andre JohanncsscnDepartment of Mathematical Sciences. Norwegian University of Science and Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

Technology. N-7491 Trondheim. NorwayAvailable online xxxxHighlights•A posteriori error estimation methodology for adaptive isogcometrie analysis usin

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

g I .R B-splincs is developed.•Supervonvergenl patch recovery of gradient field on adaptive meshes is developed.•Algorithm for compulation of true sup

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysissymptotically exact.AbstractIn this article, we address adaptive methods for isogcomctric analysis based on local refinement guided by recovery based

a posteriori error estimates.Isogeomelric analysis was introduced a decade ago and an impressive progress has been made related to many aspects of num Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

erical methods and advanced applications. However, related to adaptive mesh refinement guided hy a posteriori error estimators, rather few attempts ar

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

e pursued besides the use of classical residual based error estimators. In this article, we explore a feature common for Isogeomelric analysis (IGA).

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysisthe concept of structured mesh refinement using LR B-splines. our aim is to facilitate supereon vergence behavior for locally refined meshes as well.

Supcrconvcrgcncc behavior matches well with the use of recovery based a posteriori estimator in the Supcrconvergcnt Parch Recovery (SPR) procedure. Ho Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

wever, to our knowledge so far, the SPR procedure has nor been exploited in the KÌA community.We Stan out by addressing the existence of derivative st

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

ipereonvergent points in the computed finite clement solution based on B-splines and LR B-splines for an elliptic model problem (ID and 2D Poisson). T

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysise will be the main focus. In particular, we show that our SPR procedure for the improvement of derivatives fulfills the desired consistency criteria.

At the end. we develop a posteriori error estimator where the improved gradient obtained from the proposed recovery procedures is used.Numerical resul Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

ts are presented to illustrate the efficiency of using SPR procedure for the improvement of derivatives (or gradient) of computed solution in isogeome

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

tric analysis. Then the proposed a posteriori error estimator based adaptive refinement* Corresponding author.E-mail addresses: kum:irmO»cofc all! (M.

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysisematics. College of Charleston. Charleston, sc 29424. USA.http 7/dx.doi .ocg/1 <). 1016/j .cma.2016.11.0140045-7825/Publishcd by Elsevier B.v. This is

an open access article under the cc BY-NC-ND license (http://creativecommon.corg/licensex/by-nc-tKV4.IV).____________________________________________ Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

_____________________________________________________________________________Please cite this article in press as: M. Kumar, et al.. Superconvergent p

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

atch recovery and a posteriori error estimation technique in adaptivei sogeo me trie analysis. Comput. Methods Appl. Meeh. Engrg. (2016). hup://dx.doi

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysisooth and non-smooth elliptic benchmark problems. The focus is put on whether optimal convergence rates arc obtained in the computed solution or not. a

s well as the clfcctivity index of the proposed error estimators.Published by Elsevier B.v. This is an open access article under the cc BY-NC-ND licen Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

se (http://ciealivecommons.org/licenses/ by-nc-nd/4.0/).Keywords: Isogcomctric analysis: LR B-splincs; NL RBS: A posteriori error estimator. Adaptivit

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

y; Supcrconvcrgcnec1. IntroductionReliability and efficiency arc two major challenges in simulation based engineering. These two challenges may be add

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysisver the years. However, adaptive methods are not yet an industrial tool, partly because the need for a link to traditional Computer Aideil Design (CAD

)-systems makes this difficult in industrial practice. I lere. the use of an isogeometric analysis framework introduced by Professor Thomas J.R. Hughe Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

s (The I.'Diversity of Texas at Austin) and co-workers 11 I may facilitates more widespread adoption of this technology in industry, as adaptive mesh

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

refinement docs not require any further communication with the CAD system.Isogcomctric analysis (IGA) has been introduced in [1] as an innovative nume

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysisDF. solvers. To achieve this, authors in |l| proposed to use CAD mathematical primitives, i.e., splines and NURBS, also to represent PDF. unknowns. Th

e smoothness of splines is useful in improving the accuracy |wr degree of freedom and solving higher order PDF.S via direct approximations. Isogeomelr Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

ic methods have been used anil tested on a variety of problems of engineering interests, see 11,2| and references therein. The development on the math

Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis

ematical front started with h approximation properties of NURBS in (3]. further studies for hpk refinements in [4] and for anisotropic approximation i

ARTICLE IN PRESSEl SEVIERAvailable online at www.sciencedirect.comScienceDirectCotnput. Methods Appt. Meeh. Engrg. I I1141) MI-MIComputer methods in a