Consistent and stable meshfree Galerkin methods using the virtual element decomposition
Sign Up to like & getrecommendations! Published in 2017 at "International Journal for Numerical Methods in Engineering"
DOI: 10.1002/nme.5519
Abstract: Summary Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth… read more here.
Keywords: meshfree methods; basis functions; meshfree galerkin; galerkin methods ... See more keywords
A virtual element method for the acoustic vibration problem
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DOI: 10.1007/s00211-016-0855-5
Abstract: We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of $$\mathrm {H}(\mathrm {div})$$H(div)… read more here.
Keywords: acoustic vibration; vibration problem; virtual element;
A posteriori error estimates for the virtual element method
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DOI: 10.1007/s00211-017-0891-9
Abstract: An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully… read more here.
Keywords: error; element method; element; posteriori error ... See more keywords
Virtual element method stabilization for convection-diffusion-reaction problems using the link-cutting condition
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DOI: 10.1007/s10092-016-0180-5
Abstract: In this paper, we present a methodology for stabilizing the virtual element method applied to the convection-diffusion-reaction equation. The stabilization is carried out modifying the mesh inside the boundary layer so that the link-cutting condition… read more here.
Keywords: convection diffusion; element method; diffusion reaction; link cutting ... See more keywords
A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition
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DOI: 10.1007/s10092-019-0345-0
Abstract: In this work, we propose a virtual element method for discretizing the equations that couple the incompressible steady Stokes flow with the Darcy flow by means of the Beaver–Joseph–Saffman condition on their interface. In addition… read more here.
Keywords: element method; condition; beaver joseph; element ... See more keywords
The nonconforming virtual element method for the Navier-Stokes equations
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Computational Mathematics"
DOI: 10.1007/s10444-018-9602-z
Abstract: In this paper a unified nonconforming virtual element scheme for the Navier-Stokes equations with different dimensions and different polynomial degrees is described. Its key feature is the treatment of general elements including non-convex and degenerate… read more here.
Keywords: nonconforming virtual; element method; stokes equations; navier stokes ... See more keywords
A fully coupled scheme using virtual element method and finite volume for poroelasticity
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DOI: 10.1007/s10596-019-09831-w
Abstract: In this paper, we design and study a fully coupled numerical scheme for the poroelasticity problem modeled through Biot’s equations. The classical way to numerically solve this system is to use a finite element method… read more here.
Keywords: element method; finite volume; method; element ... See more keywords
A Virtual Element Method for the Wave Equation on Curved Edges in Two Dimensions
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DOI: 10.1007/s10915-021-01683-w
Abstract: In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe… read more here.
Keywords: curved edges; wave equation; geometry; element method ... See more keywords
A Nonconforming Virtual Element Method for a Fourth-order Hemivariational Inequality in Kirchhoff Plate Problem
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DOI: 10.1007/s10915-022-01759-1
Abstract: This paper is devoted to a fourth-order hemivariational inequality for a Kirchhoff plate problem. A solution existence and uniqueness result is proved for the hemivariational inequality through the analysis of a corresponding minimization problem. A… read more here.
Keywords: hemivariational inequality; virtual element; problem; order ... See more keywords
B-bar virtual element method for nearly incompressible and compressible materials
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DOI: 10.1007/s11012-020-01218-x
Abstract: We present a B-bar formulation of the virtual element method (VEM) for the analysis of both nearly incompressible and compressible materials. The material stiffness is decomposed into dilatational and deviatoric parts, and only the deviatoric… read more here.
Keywords: nearly incompressible; compressible materials; element method; element ... See more keywords
A modified nonconforming virtual element with BDM-like reconstruction for the Navier-Stokes equations
Sign Up to like & getrecommendations! Published in 2021 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2021.05.014
Abstract: Abstract In this paper, we develop a modified nonconforming virtual element with a divergence-free BDM-like reconstruction for the Navier-Stokes problem. The main idea is to use a divergence preserving velocity reconstruction operator in the discretization… read more here.
Keywords: reconstruction; modified nonconforming; nonconforming virtual; virtual element ... See more keywords