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arXiv · 2506.05886

Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation

Matteo Ferrari·Ilaria Perugia·Enrico Zampa
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Abstract

In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We analyze the method, showing its stability without imposing any restrictions on the mesh size or time step, and proving quasi-optimal convergence for any choice of space-time tensor product discrete spaces that satisfies standard approximation assumptions. Numerical examples are provided to support the theoretical findings.

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Matteo Ferrari, Ilaria Perugia, Enrico Zampa. 2025-06-06. Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation. https://arxiv.org/abs/2506.05886

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