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Intrinsic unconditional stability in space–time isogeometric approximation of the acoustic wave equation in second-order formulation.

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Title: Intrinsic unconditional stability in space–time isogeometric approximation of the acoustic wave equation in second-order formulation.
Authors: Ferrari, Matteo1 (AUTHOR) matteo.ferrari@univie.ac.at, Perugia, Ilaria1 (AUTHOR) ilaria.perugia@univie.ac.at
Source: Mathematical Models & Methods in Applied Sciences. Mar2026, Vol. 36 Issue 3, p561-599. 39p.
Subjects: Wave equation, Isogeometric analysis, Variational principles, Stability theory, Error analysis in mathematics, Numerical calculations, Splines
Abstract: In this paper, we present a novel space–time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [N. J. Walkington, Combined DG-CG time stepping for wave equations, SIAM J. Numer. Anal. 52 (2014) 1398–1417], with an exponential weight introduced in the time integrals. Consistency requires C 1 regularity in time and C 0 in space. The unconditional stability of the space–time method for conforming discrete spaces arises naturally from the variational structure itself, rather than from any artificial stabilization mechanisms. The error analysis is developed in the case of tensor-product approximation spaces with approximation in time carried out using spline functions. In particular, we prove optimal convergence rates for C 1 -regular splines of even polynomial degree, and provide numerical evidence suggesting that the same behavior holds for splines with maximal regularity, irrespective of the degree. Numerical results are provided to support the theoretical findings and demonstrate the sharpness of the estimates. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Models & Methods in Applied Sciences is the property of World Scientific Publishing Company 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: Intrinsic unconditional stability in space–time isogeometric approximation of the acoustic wave equation in second-order formulation.
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+Models+%26+Methods+in+Applied+Sciences%22">Mathematical Models & Methods in Applied Sciences</searchLink>. Mar2026, Vol. 36 Issue 3, p561-599. 39p.
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  Data: <searchLink fieldCode="DE" term="%22Wave+equation%22">Wave equation</searchLink><br /><searchLink fieldCode="DE" term="%22Isogeometric+analysis%22">Isogeometric analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+principles%22">Variational principles</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+calculations%22">Numerical calculations</searchLink><br /><searchLink fieldCode="DE" term="%22Splines%22">Splines</searchLink>
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  Data: In this paper, we present a novel space–time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [N. J. Walkington, Combined DG-CG time stepping for wave equations, SIAM J. Numer. Anal. 52 (2014) 1398–1417], with an exponential weight introduced in the time integrals. Consistency requires C 1 regularity in time and C 0 in space. The unconditional stability of the space–time method for conforming discrete spaces arises naturally from the variational structure itself, rather than from any artificial stabilization mechanisms. The error analysis is developed in the case of tensor-product approximation spaces with approximation in time carried out using spline functions. In particular, we prove optimal convergence rates for C 1 -regular splines of even polynomial degree, and provide numerical evidence suggesting that the same behavior holds for splines with maximal regularity, irrespective of the degree. Numerical results are provided to support the theoretical findings and demonstrate the sharpness of the estimates. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematical Models & Methods in Applied Sciences is the property of World Scientific Publishing Company 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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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1142/S0218202526500089
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 39
        StartPage: 561
    Subjects:
      – SubjectFull: Wave equation
        Type: general
      – SubjectFull: Isogeometric analysis
        Type: general
      – SubjectFull: Variational principles
        Type: general
      – SubjectFull: Stability theory
        Type: general
      – SubjectFull: Error analysis in mathematics
        Type: general
      – SubjectFull: Numerical calculations
        Type: general
      – SubjectFull: Splines
        Type: general
    Titles:
      – TitleFull: Intrinsic unconditional stability in space–time isogeometric approximation of the acoustic wave equation in second-order formulation.
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            NameFull: Ferrari, Matteo
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            NameFull: Perugia, Ilaria
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            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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              Value: 36
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            – TitleFull: Mathematical Models & Methods in Applied Sciences
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