Equivalent projectors for virtual element methods

By Bashir Ahmad, Ahmed Alsaedi, Franco Brezzi, L. Donatella Marini, Alessandro Russo. Computers and Mathematics with Applications, 2013

621 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/01b19363d50aeaa00ea575f9fe1092e033bc660e

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Conforming and nonconforming virtual element methods for elliptic problems (2015, positive): “The framework is based on assuming that the L 2 -projector onto the polynomial subspace of the virtual element space is computable, in this respect following the approach of [1, 8].”
Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, methodology): “The Virtual Element Method has been applied successfully for a large range of problems, for instance a non exhaustive list being [4, 20, 5, 1, 11, 18, 2, 27, 12, 29, 10, 38, 3].”
Orthogonal polynomials in badly shaped polygonal elements for the Virtual Element Method (2017, positive): “In the definition of the VEM space we ask that (q, φi)E = (q,Π ∇ k φi)E , ∀q ∈ Pk (E) /Pk−2 (E) and this is the way we can compute the last row of the matrix C and consequantly the matrix pC [40, 41].”
Virtual element method for quasilinear elliptic problems (2017, neutral): “retisation of problem (1.3), using general polygonal and polyhedral decompositions of in two and three dimensions, respectively. We start by recalling the denition of the virtual element spaces from [1, 17]. 2.1. The Discrete Spaces. The denition of the virtual element method relies on the availabil”
Virtual element methods for parabolic problems on polygonal meshes (2015, methodology): “Analogously, as shown in [24, 30], we set for all vh, wh ∈ Wk|K mKh (vh, wh) := ( K ,kvh, K ,kwh) + β |K| ( ((I − K ,k)vh, (I − K ,k)wh) )”
A multigrid algorithm for the $p$-version of the Virtual Element Method (2017, methodology): “[3, 17, 19], where the internal dofs are defined as the (scaled) moments with respect to the monomial basis (2.”
The virtual element method for discrete fracture network simulations (2014, positive): “In the present work the newly conceived Virtual Element Method is in charge for the space discretization on each fracture.”
The Hitchhiker's Guide to the Virtual Element Method (2014, methodology): “In [1] it is shown that we can take the following degrees of freedom in Vk.”
Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions (2018, methodology): “We here mention, in addition to the ones above, a sample of papers [1, 4, 8, 13, 17, 19, 22, 27] and refer to [25] for a more complete survey of the existing VEM literature.”
Virtual element for the buckling problem of Kirchhoff–Love plates (2019, background): “[1]) to build a computable right hand of the buckling eigenvalue problem.”
Extended virtual element method for the Laplace problem with singularities and discontinuities (2019, methodology): “The following mesh regularity assumptions are usually considered in the convergence analysis of the conforming VEM [9, 12].”