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Inf–Sup Stable Space–Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation.

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Title: Inf–Sup Stable Space–Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation.
Authors: Ferrari, Matteo1 (AUTHOR) matteo.ferrari@univie.ac.at, Perugia, Ilaria1 (AUTHOR) ilaria.perugia@univie.ac.at, Zampa, Enrico1 (AUTHOR) enrico.zampa@univie.ac.at
Source: Journal of Scientific Computing. Jun2026, Vol. 107 Issue 3, p1-32. 32p.
Abstract: In this paper, we present a conforming space–time discretization of the wave equation based on a first-order-in-time variational formulation. Our method extends the scheme of French and Peterson (1996), incorporating exponential weights in time, which yield an inf–sup stability condition for arbitrary choices of discrete subspaces, including spline spaces, without restrictions on the mesh size or time step. Moreover, using elliptic projections, we derive optimal convergence rates in both the energy and L 2 norms for sufficiently smooth solutions and for any choice of space–time tensor product subspaces satisfying standard approximation assumptions. Numerical examples are provided to support the theoretical findings. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Scientific Computing 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: Inf–Sup Stable Space–Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation.
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  Data: <searchLink fieldCode="AR" term="%22Ferrari%2C+Matteo%22">Ferrari, Matteo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> matteo.ferrari@univie.ac.at</i><br /><searchLink fieldCode="AR" term="%22Perugia%2C+Ilaria%22">Perugia, Ilaria</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ilaria.perugia@univie.ac.at</i><br /><searchLink fieldCode="AR" term="%22Zampa%2C+Enrico%22">Zampa, Enrico</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> enrico.zampa@univie.ac.at</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Scientific+Computing%22">Journal of Scientific Computing</searchLink>. Jun2026, Vol. 107 Issue 3, p1-32. 32p.
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  Data: In this paper, we present a conforming space–time discretization of the wave equation based on a first-order-in-time variational formulation. Our method extends the scheme of French and Peterson (1996), incorporating exponential weights in time, which yield an inf–sup stability condition for arbitrary choices of discrete subspaces, including spline spaces, without restrictions on the mesh size or time step. Moreover, using elliptic projections, we derive optimal convergence rates in both the energy and L 2 norms for sufficiently smooth solutions and for any choice of space–time tensor product subspaces satisfying standard approximation assumptions. Numerical examples are provided to support the theoretical findings. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Scientific Computing 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/s10915-026-03293-w
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              Text: Jun2026
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              Y: 2026
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