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The nonconforming virtual element method [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2016 We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the
Ayuso De Dios, B +2 more
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The Virtual Element Method for the Dam Foundation With Joint
Frontiers in Earth Science, 2022 The contact is a typical non-linear problem that exists in various projects. For traditional three-node triangular mesh and four-node quadrilateral mesh, the accuracy and convergence of the calculation results are affected by the quality of the mesh. The
Yinghao Sun +7 more
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AN IMPROVED DISTINCT ELEMENT METHOD FOR HIGH PACKING FRACTION STOCHASTIC MEDIA MODELING [PDF]
EPJ Web of Conferences, 2021 Due to the generality and flexibility of Monte Carlo method in geometric modeling, Monte Carlo method plays an important role in accurate simulation of random media.
Feng Zhiyuan, An Nan, Wang Kan
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Virtual Elements on polyhedra with a curved face
Bulletin of Mathematical Sciences, 2023 We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges.
Franco Brezzi, L. Donatella Marini
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Virtual element method for quasilinear elliptic problems [PDF]
IMA Journal of Numerical Analysis, 2019 Abstract A virtual element method for the quasilinear equation $-\textrm{div} ({\boldsymbol \kappa }(u)\operatorname{grad} u)=f$ using general polygonal and polyhedral meshes is presented and analysed. The nonlinear coefficient is evaluated with the piecewise polynomial projection of the virtual element ansatz.
Cangiani A. +3 more
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An AR Map Virtual–Real Fusion Method Based on Element Recognition
ISPRS International Journal of Geo-Information, 2023 The application of AR to explore augmented map representation has become a research hotspot due to the growing application of AR in maps and geographic information in addition to the rising demand for automated map interpretation.
Zhangang Wang
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Superconvergent gradient recovery for virtual element methods [PDF]
Mathematical Models and Methods in Applied Sciences, 2019 Virtual element method is a new promising finite element method using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In this paper, we take a different viewpoint. We try to uncover the superconvergent property of virtual element methods by doing some local post-processing only on the degrees of ...
Guo, Hailong, Xie, Cong, Zhao, Ren
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Basic principles of mixed Virtual Element Methods [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2014 The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n-1)-Cochains). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element ...
F Brezzi, RS Falk, LD Marini
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A free‐cutting mesh strategy for optimal shape synthesis in magnetics
IET Science, Measurement & Technology, 2022 The authors propose an innovative technique for dealing with optimal shape design problems that exploits the flexibility of the virtual element method in generating meshes composed of general polygonal and polyhedral elements.
F. Dassi, P. Di Barba, A. Russo
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Some error analysis on virtual element methods [PDF]
Calcolo, 2018 Some error analysis on virtual element methods including inverse inequalities, norm equivalence, and interpolation error estimates are presented for polygonal meshes which admits a virtual quasi-uniform triangulation.
Chen, Long, Huang, Jianguo
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