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arXiv · 2211.02692

High-Order Spline Upwind for Space-Time Isogeometric Analysis

Gabriele Loli·Giancarlo Sangalli·Paolo Tesini
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Abstract

We propose an innovative isogeometric space-time method for the heat equation, with smooth splines approximation in both space and time. To enhance the stability of the method we add a stabilizing term, based on a linear combination of high-order artificial diffusions. This term is designed in order to make the linear system lower block-triangular, that is, lower triangular with respect to time. In order to keep optimal accuracy, the stabilization terms are further weighted in terms of the residual. Through a series of numerical experiments, we validate the method's capability, showcasing its stability and accuracy.

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Gabriele Loli, Giancarlo Sangalli, Paolo Tesini. 2022-11-04. High-Order Spline Upwind for Space-Time Isogeometric Analysis. https://arxiv.org/abs/2211.02692

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