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arXiv · 2409.11639

Spline-based solution transfer for space-time methods in 2D+t

Logan Larose·Jude T. Anderson·David M. Williams
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Abstract

This work introduces a new solution-transfer process for slab-based space-time finite element methods. The new transfer process is based on Hsieh-Clough-Tocher (HCT) splines and satisfies the following requirements: (i) it maintains high-order accuracy up to 4th order, (ii) it preserves a discrete maximum principle, (iii) it asymptotically enforces mass conservation, and (iv) it constructs a smooth, continuous surrogate solution in between space-time slabs. While many existing transfer methods meet the first three requirements, the fourth requirement is crucial for enabling visualization and boundary condition enforcement for space-time applications. In this paper, we derive an error bound for our HCT spline-based transfer process. Additionally, we conduct numerical experiments quantifying the conservative nature and order of accuracy of the transfer process. Lastly, we present a qualitative evaluation of the visualization properties of the smooth surrogate solution.

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Logan Larose, Jude T. Anderson, David M. Williams. 2024-09-18. Spline-based solution transfer for space-time methods in 2D+t. https://arxiv.org/abs/2409.11639

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