Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

[EN] An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a ¿smooth + singular¿ decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.Stephane Bordas would like to thank the partial financial support of the Royal Academy of Engineering and of the Leverhulme Trust for his Senior Research Fellowship Towards the next generation surgical simulators as well as the financial support for Octavio A. Gonzalez-Estrada and Stephane Bordas from the UK Engineering Physical Science Research Council (EPSRC) under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method. Stephane Bordas also thanks partial financial support of the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) and the FP7 Initial Training Network Funding under grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology, INSIST". This work has been carried out within the framework of the research project DPI2010-20542 of the Ministerio de Ciencia e Innovacion (Spain). The financial support from Universitat Politecnica de Valencia, PROMETEO/2012/023 and Generalitat Valenciana are also acknowledged.González Estrada, OA.; Natarajan, S.; J.J. Ródenas; Nguyen-Xuan, H.; Bordas, S. (2013). Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Computational Mechanics. 52(1):37-52. https://doi.org/10.1007/s00466-012-0795-6S3752521Liu GR, Dai KY, Nguyen TT (2006) A smoothed finite element method for mechanics problems. 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Int J Numer Methods Eng 76(4): 545–571. doi: 10.1002/nme.2313Panetier J, Ladevèze P, Chamoin L (2010) Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM. Int J Numer Methods Eng 81(6): 671–700Barros FB, Proenca SPB, de Barcellos CS (2004) On error estimator and p-adaptivity in the generalized finite element method. Int J Numer Methods Eng 60(14):2373–2398. doi: 10.1002/nme.1048Nguyen-Thoi T, Liu G, Nguyen-Xuan H, Nguyen-Tran C (2011) Adaptive analysis using the node-based smoothed finite element method (NS-FEM). Int J Numer Methods Biomed Eng 27(2): 198–218. doi: 10.1002/cnmGonzález-Estrada OA, Ródenas JJ, Bordas SPA, Duflot M, Kerfriden P, Giner E (2012) On the role of enrichment and statical admissibility of recovered fields in a-posteriori error estimation for enriched finite element methods. Eng Comput 29(8)Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2): 337–357Ródenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2010) Accurate recovery-based upper error bounds for the extended finite element framework. Comput Methods Appl Mech Eng 199(37–40): 2607–2621Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plate in extension. J Appl Mech 19: 526–534Szabó BA, Babuška I (1991) Finite element analysis. Wiley, New YorkBarber JR. (2010) Elasticity. Series: solid mechanics and its application, 3rd edn. Springer, DordrechtChen JS, Wu CT, Yoon S, You Y (2001) A stabilized conforming nodal integration for Galerki mesh-free methods. Int J Numer Methods Eng 50: 435–466Yoo J, Moran B, Chen J (2004) Stabilized conforming nodal integration in the natural element method. Int J Numer Methods Eng 60: 861–890Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33(7): 1331–1364Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33(7): 1365–1382Wiberg NE, Abdulwahab F (1993) Patch recovery based on superconvergent derivatives and eóuilibrium. Int J Numer Methods Eng 36(16): 2703–2724. doi: 10.1002/nme.1620361603Blacker T, Belytschko T (1994) Superconvergent patch recovery with eóuilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37(3): 517–536Stein E, Ramm E, Rannacher R (2003) Error-controlled adaptive finite elements in solid mechanics. Wiley, ChichesterDuflot M, Bordas SPA (2008) A posteriori error estimation for extended finite elements by an extended global recovery. 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In: Khalili N, Valliappan S, Li ó, Russell A (eds) 9th World congress on computational mechanics (WCCM9). 4th Asian Pacific Congress on computational methods (APCOM2010). Centre for Infrastructure Engineering and SafetyRódenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2007) Upper bounds of the error in the extended finite element method by using an eóuilibrated-stress patch recovery technique. In: International conference on adaptive modeling and simulation (ADMOS 2007). International Center for Numerical Methods in Engineering (CIMNE), pp 210–213Menk A, Bordas S (2010) Numerically determined enrichment function for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals. Int J Numer Methods Eng 83: 805–828Menk A, Bordas S (2011) Crack growth calculations in solder joints based on microstructural phenomena with X-FEM. 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Fungal Planet description sheets : 951–1041

Novel species of fungi described in this study include those from various countries as follows: Antarctica,Apenidiella antarctica from permafrost, Cladosporium fildesense from an unidentified marine sponge. Argentina,Geastrum wrightii on humus in mixed forest. Australia, Golovinomyces glandulariae on Glandularia aristigera,Neoanungitea eucalyptorum on leaves of Eucalyptus grandis, Teratosphaeria corymbiicola on leaves of Corymbiaficifolia, Xylaria eucalypti on leaves of Eucalyptus radiata. Brazil, Bovista psammophila on soil, Fusarium awaxy onrotten stalks of Zea mays, Geastrum lanuginosum on leaf litter covered soil, Hermetothecium mikaniae-micranthae(incl. Hermetothecium gen. nov.) on Mikania micrantha, Penicillium reconvexovelosoi in soil, Stagonosporopsis vannacciifrom pod of Glycine max. British Virgin Isles, Lactifluus guanensis on soil. Canada, Sorocybe oblongisporaon resin of Picea rubens. Chile, Colletotrichum roseum on leaves of Lapageria rosea. China, Setophoma cavernafrom carbonatite in Karst cave. Colombia, Lareunionomyces eucalypticola on leaves of Eucalyptus grandis. CostaRica, Psathyrella pivae on wood. Cyprus, Clavulina iris on calcareous substrate. France, Chromosera ambiguaand Clavulina iris var. occidentalis on soil. French West Indies, Helminthosphaeria hispidissima on dead wood.Guatemala, Talaromyces guatemalensis in soil. Malaysia, Neotracylla pini (incl. Tracyllales ord. nov. and Neotracyllagen. nov.) and Vermiculariopsiella pini on needles of Pinus tecunumanii. New Zealand, Neoconiothyriumviticola on stems of Vitis vinifera, Parafenestella pittospori on Pittosporum tenuifolium, Pilidium novae-zelandiaeon Phoenix sp. Pakistan, Russula quercus-floribundae on forest floor. Portugal, Trichoderma aestuarinum fromsaline water. Russia, Pluteus liliputianus on fallen branch of deciduous tree, Pluteus spurius on decaying deciduous wood or soil. South Africa, Alloconiothyrium encephalarti, Phyllosticta encephalarticola and Neothyrostromaencephalarti (incl. Neothyrostroma gen. nov.) on leaves of Encephalartos sp., Chalara eucalypticola on leaf spots ofEucalyptus grandis x urophylla, Clypeosphaeria oleae on leaves of Olea capensis, Cylindrocladiella postalofficiumon leaf litter of Sideroxylon inerme, Cylindromonium eugeniicola (incl. Cylindromonium gen. nov.) on leaf litter ofEugenia capensis, Cyphellophora goniomatis on leaves of Gonioma kamassi, Nothodactylaria nephrolepidis (incl.Nothodactylaria gen. nov. and Nothodactylariaceae fam. nov.) on leaves of Nephrolepis exaltata, Falcocladiumeucalypti and Gyrothrix eucalypti on leaves of Eucalyptus sp., Gyrothrix oleae on leaves of Olea capensis subsp.macrocarpa, Harzia metro-sideri on leaf litter of Metrosideros sp., Hippopotamyces phragmitis (incl. Hippopotamycesgen. nov.) on leaves of Phragmites australis, Lectera philenopterae on Philenoptera violacea, Leptosilliamayteni on leaves of Maytenus heterophylla, Lithohypha aloicola and Neoplatysporoides aloes on leaves of Aloesp., Millesimomyces rhoicissi (incl. Millesimomyces gen. nov.) on leaves of Rhoicissus digitata, Neodevriesiastrelitziicola on leaf litter of Strelitzia nicolai, Neokirramyces syzygii (incl. Neokirramyces gen. nov.) on leaf spots of Syzygium sp., Nothoramichloridium perseae (incl. Nothoramichloridium gen. nov. and Anungitiomycetaceae fam.nov.) on leaves of Persea americana, Paramycosphaerella watsoniae on leaf spots of Watsonia sp., Penicilliumcuddlyae from dog food, Podocarpomyces knysnanus (incl. Podocarpomyces gen. nov.) on leaves of Podocarpusfalcatus, Pseudocercospora heteropyxidicola on leaf spots of Heteropyxis natalensis, Pseudopenidiella podocarpi,Scolecobasidium podocarpi and Ceramothyrium podocarpicola on leaves of Podocarpus latifolius, Scolecobasidiumblechni on leaves of Blechnum capense, Stomiopeltis syzygii on leaves of Syzygium chordatum, Strelitziomycesknysnanus (incl. Strelitziomyces gen. nov.) on leaves of Strelitzia alba, Talaromyces clemensii from rotting wood ingoldmine, Verrucocladosporium visseri on Carpobrotus edulis. Spain, Boletopsis mediterraneensis on soil, Calycinacortegadensisi on a living twig of Castanea sativa, Emmonsiellopsis tuberculata in fluvial sediments, Mollisia cortegadensison dead attached twig of Quercus robur, Psathyrella ovispora on soil, Pseudobeltrania lauri on leaf litterof Laurus azorica, Terfezia dunensis in soil, Tuber lucentum in soil, Venturia submersa on submerged plant debris.Thailand, Cordyceps jakajanicola on cicada nymph, Cordyceps kuiburiensis on spider, Distoseptispora caricis onleaves of Carex sp., Ophiocordyceps khonkaenensis on cicada nymph. USA, Cytosporella juncicola and Davidiellomycesjuncicola on culms of Juncus effusus, Monochaetia massachusettsianum from air sample, Neohelicomycesmelaleucae and Periconia neobrittanica on leaves of Melaleuca styphelioides x lanceolata, Pseudocamarosporiumeucalypti on leaves of Eucalyptus sp., Pseudogymnoascus lindneri from sediment in a mine, Pseudogymnoascusturneri from sediment in a railroad tunnel, Pulchroboletus sclerotiorum on soil, Zygosporium pseudomasonii onleaf of Serenoa repens. Vietnam, Boletus candidissimus and Veloporphyrellus vulpinus on soil. Morphological andculture characteristics are supported by DNA barcodes