Trevor Giannini
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Trevor Giannini has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Jehanzeb Hameed Chaudhry
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA
2 shared publications - Simon Tavener
Colorado State University, Fort Collins, USA
2 shared publications - Zachary Stevens
The University of New Mexico, Albuquerque, USA
2 shared publications Don Estep
1 shared publication- Donald Estep
Simon Fraser University, Burnaby, Canada
1 shared publication
Latest Publications
- 4 February 2023
- Published by Springer Nature in BIT Numerical Mathematics
- Vol. 63 (1) , 1-32
Error estimation for the time to a threshold value in evolutionary partial differential equations
- 4 February 2023
- Published by Springer Nature in BIT Numerical Mathematics
- Vol. 63 (1) , 1-32
Error estimation for the time to a threshold value in evolutionary partial differential equations
- Open Access
Error estimation for the time to a threshold value in evolutionary partial differential equations
We develop an \textit{a posteriori} error analysis for a numerical estimate of the time at which a functional of the solution to a partial differential equation (PDE) first achieves a threshold value on a given time interval. This quantity of interest (QoI) differs from classical QoIs which are modeled as bounded linear (or nonlinear) functionals {of the solution}. Taylor's theorem and an adjoint-based \textit{a posteriori} analysis is used to derive computable and accurate error estimates in the case of semi-linear parabolic and hyperbolic PDEs. The accuracy of the error estimates is demonstrated through numerical solutions of the one-dimensional heat equation and linearized shallow water equations (SWE), representing parabolic and hyperbolic cases, respectively.
Open AccessError estimation for the time to a threshold value in evolutionary partial differential equations
We develop an \textit{a posteriori} error analysis for a numerical estimate of the time at which a functional of the solution to a partial differential equation (PDE) first achieves a threshold value on a given time interval. This quantity of interest (QoI) differs from classical QoIs which are modeled as bounded linear (or nonlinear) functionals {of the solution}. Taylor's theorem and an adjoint-based \textit{a posteriori} analysis is used to derive computable and accurate error estimates in the case of semi-linear parabolic and hyperbolic PDEs. The accuracy of the error estimates is demonstrated through numerical solutions of the one-dimensional heat equation and linearized shallow water equations (SWE), representing parabolic and hyperbolic cases, respectively.