The nonconforming virtual element method

By Blanca Ayuso de Dios, Konstantin Lipnikov, Gianmarco Manzini. 2014

301 citations recorded by the source corpus.

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 equivalence with a family of mimetic finite difference methods.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/246f126ba2353865e241df32cf858662e9680bca

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A multigrid algorithm for the $p$-version of the Virtual Element Method (2017, methodology): “refer to [7] and [29], respectively. Moreover, several variants of the Virtual Element Method, including mixed, H(div) and H(curl)-conforming, serendipity and nonconforming VEMs have been proposed in [11,14,18{20,33,39,56]. All the above mentioned contributions focus on the h{version of the Virtual ”
Conforming and nonconforming virtual element methods for elliptic problems (2015, unknown): “(E): The proof that the combined set of degrees of freedom is unisolvent for the conforming space is given in [1], and for the nonconforming space follows exactly as the original unisolvence proof in [3]. It is based on the observation that each space denes its elements as those functions which solv”
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods (2016, methodology): “17)), whereas the stabilization r sT is a special instance of the one appearing in the right-hand side of ([2], Eq.”
A Hybrid High-Order method for the incompressible Navier-Stokes equations based on Temam's device (2018, unknown): “The HHO method we present here can therefore be considered as a higher-order extension of the HMM scheme for Navier–Stokes as in [32, 33] As shown in [24, Section 4], the HHO method for diﬀusion equations is very close to the non-conforming Virtual Element Method (VEM) [4] and the high-order mixed M”
A Plane Wave Virtual Element Method for the Helmholtz Problem (2015, background): “The basic VEM introduced on the Poisson problem has then been extended to highly regular [11], non conforming [2] and discontinuous approximating spaces [16], to general elliptic [8] and mixed problems [6,7,14], as well as to Stokes [1], plate problems [15], linear and non linear elasticity [5, 10, ”
Virtual element method for quasilinear elliptic problems (2017, unknown): “ularity assumption used in the linear setting [6, 17], allowing for very general polygonal and polyhedral meshes. Virtual element methods for linear elliptic problems are now well-established, see eg.[6, 11, 1, 10, 5, 17, 13] and [26] for a simple implementation. See also [7] for an extension to mes”
Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions (2018, result): “We here mention, in addition to the ones above, a sample of papers [1, 9, 18, 4, 12, 16, 26, 22] and refer to [24] for a more complete survey of the existing VEM literature.”