The virtual element method in 50 lines of MATLAB

Sutton, Oliver J.

doi:10.1007/s11075-016-0235-3

Cited by 80 publications

(50 citation statements)

References 32 publications

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“…We generate random voronoi-mesh discretization exploiting polymesher (cf. [28,29]) Figure 4. The rate of convergences in L 2 -and H 1 -norms are displayed in Figure 5, which have a very good agreement with theoretically estimated results.…”

Section: Testmentioning

confidence: 99%

Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

Adak

Natarajan

Kumar

2018

Numerical Methods Partial

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In this article, we discuss and analyze new conforming virtual element methods (VEMs) for the approximation of semilinear parabolic problems on convex polygonal meshes in two spatial dimension. The spatial discretization is based on polynomial and suitable nonpolynomial functions, and a Euler backward scheme is employed for time discretization. The discrete formulation of both the proposed schemes—semidiscrete and fully discrete (with time discretization) is discussed in detail, and the unique solvability of the resulted schemes is discussed. A priori error estimates for the proposed schemes (semidiscrete and fully discrete) in H1‐ and L2‐norms are derived under the assumption that the source term f is Lipschitz continuous. Some numerical experiments are conducted to illustrate the performance of the proposed scheme and to confirm the theoretical convergence rates.

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Section: Testmentioning

confidence: 99%

Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

Adak

Natarajan

Kumar

2018

Numerical Methods Partial

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“…On the contrary, since Veamy's scope is research and teaching, in its design we wanted a direct and balanced correspondence between theory and implementation. In this sense, Veamy is very similar in its spirit to the 50-line MATLAB implementation of the VEM [29]. However, compared to this MATLAB implementation, Veamy is an improvement in the following aspects:…”

Section: Introductionmentioning

confidence: 91%

Veamy: an extensible object-oriented C++ library for the virtual element method

et al. 2019

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This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in two dimensions have been chosen as the starting stage for the development of this library. The theory of the VEM, upon which Veamy is built, is presented using a notation and a terminology that resemble the language of the finite 2 Ortiz-Bernardin et al. element method (FEM) in engineering analysis. Several examples are provided to demonstrate the usage of Veamy, and in particular, one of them features the interaction between Veamy and the polygonal mesh generator PolyMesher. A computational performance comparison between VEM and FEM is also conducted. Veamy is free and open source software.

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“…Abaqus package is available for nSFEM [183]. VEM has been developed and tested in MATLAB and Abaqus packages [184,185]. MATLAB code on PSBFEM is used in [186].…”

Section: Software Packagesmentioning

confidence: 99%

A Brief Review on Polygonal/Polyhedral Finite Element Methods

Perumal

2018

Mathematical Problems in Engineering

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This paper provides brief review on polygonal/polyhedral finite elements. Various techniques, together with their advantages and disadvantages, are listed. A comparison of various techniques with the recently proposed Virtual Node Polyhedral Element (VPHE) is also provided. This review would help the readers to understand the various techniques used in formation of polygonal/polyhedral finite elements.

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The virtual element method in 50 lines of MATLAB

Cited by 80 publications

References 32 publications

Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

Veamy: an extensible object-oriented C++ library for the virtual element method

A Brief Review on Polygonal/Polyhedral Finite Element Methods

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