Stability of conforming space--time isogeometric methods for the wave equation.
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| Title: | Stability of conforming space--time isogeometric methods for the wave equation. |
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| Authors: | Ferrari, Matteo1 (AUTHOR), Fraschini, Sara2 (AUTHOR) |
| Source: | Mathematics of Computation. Mar2026, Vol. 95 Issue 358, p683-719. 37p. |
| Subjects: | Stability criterion, Wave equation, Numerical analysis, Dynamic stability, Finite element method, Mathematical regularization, Splines, Isogeometric analysis |
| Abstract: | We consider a family of conforming space–time finite element discretizations for the wave equation based on splines of maximal regularity in time. Traditional techniques may require a Courant–Friedrichs–Lewy (CFL) condition to guarantee stability. Recent works by O. Steinbach and M. Zank (2019), and S. Fraschini, G. Loli, A. Moiola, and G. Sangalli (2024), have introduced unconditionally stable schemes by adding nonconsistent penalty terms to the underlying bilinear form. Stability and error analysis have been carried out for lowest order discrete spaces. While higher order methods have shown promising properties through numerical testing, their rigorous analysis was still missing. In this paper, we address this stability analysis by studying the properties of the condition number of a family of matrices associated with the time discretization. For each spline order, we derive explicit estimates of both the CFL condition required in the unstabilized case and the penalty term that minimises the consistency error in the stabilized case. Numerical tests confirm the sharpness of our results. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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