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On a space-time implementation of the wave equation using virtual elements.

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Title: On a space-time implementation of the wave equation using virtual elements.
Authors: Wriggers, P.1,2 (AUTHOR) wriggers@ikm.uni-hannover.de, Junker, Ph.1,2 (AUTHOR) junker@ikm.uni-hannover.de
Source: Computational Mechanics. Jan2026, Vol. 77 Issue 1, p197-211. 15p.
Subjects: Spacetime, Wave equation, Structural components, Finite element method, Discretization methods, Numerical analysis, Hamilton's principle function
Abstract: The virtual element method (VEM) was developed not too long ago, starting with the paper (Beirão-da-Veiga et al. in SIAM J Numer Anal 51:794–812, 2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements, however has so far not applied to space-time formulations for one-dimensional structural elements like strings, trusses and beams. Here we study several VEM elements suitable for space-time formulations that are build upon the Hamilton's principle. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns. Furthermore, we show that the property of VEM to deal with non-conforming meshes is of special interest for holistic space time formulation: VEM formulations allow locally varying time discretizations (time increments) in a natural and efficient way. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Wriggers%2C+P%2E%22">Wriggers, P.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> wriggers@ikm.uni-hannover.de</i><br /><searchLink fieldCode="AR" term="%22Junker%2C+Ph%2E%22">Junker, Ph.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> junker@ikm.uni-hannover.de</i>
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  Data: <searchLink fieldCode="JN" term="%22Computational+Mechanics%22">Computational Mechanics</searchLink>. Jan2026, Vol. 77 Issue 1, p197-211. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Spacetime%22">Spacetime</searchLink><br /><searchLink fieldCode="DE" term="%22Wave+equation%22">Wave equation</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+components%22">Structural components</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton's+principle+function%22">Hamilton's principle function</searchLink>
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  Data: The virtual element method (VEM) was developed not too long ago, starting with the paper (Beirão-da-Veiga et al. in SIAM J Numer Anal 51:794–812, 2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements, however has so far not applied to space-time formulations for one-dimensional structural elements like strings, trusses and beams. Here we study several VEM elements suitable for space-time formulations that are build upon the Hamilton's principle. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns. Furthermore, we show that the property of VEM to deal with non-conforming meshes is of special interest for holistic space time formulation: VEM formulations allow locally varying time discretizations (time increments) in a natural and efficient way. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00466-024-02556-3
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        Text: English
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        StartPage: 197
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      – SubjectFull: Spacetime
        Type: general
      – SubjectFull: Wave equation
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      – SubjectFull: Structural components
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      – SubjectFull: Hamilton's principle function
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              Text: Jan2026
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