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arXiv · 2402.08291

On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates

Richard Löscher·Olaf Steinbach·Marco Zank
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Abstract

In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependent partial differential equations. It turns out that the stability constant depends linearly on the finite element mesh parameter, but in most cases, we can show optimal convergence. We present a series of numerical experiments which illustrate the theoretical findings.

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Richard Löscher, Olaf Steinbach, Marco Zank. 2024-02-13. On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates. https://arxiv.org/abs/2402.08291

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