Adaptive finite element methods (AFEM) represent a pivotal advancement in numerical analysis by dynamically refining computational meshes to achieve greater solution accuracy. These methods are ...

The field of optimal control in partial differential equations (PDEs) focuses on determining the best possible control strategies to influence systems described by PDEs and to achieve specific ...

General aspects of polynomial interpolation theory. Formulations in different basis, e.g. Lagrange, Newton etc. and their approximation and computational properties ...

In this paper, we present new error bounds for the Lanczos method and the shift-and-invert Lanczos method for computing e -τA v for a large sparse symmetric positive ...

We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order a posteriori estimates controlling the ...

Due to the chaotic nature of the atmosphere, weather forecasts, even with ever improving numerical weather prediction models, eventually lose all skill. Meteorologists have a strong desire to better ...

"Taxonomy of purposes, methods, and recommendations for vulnerability analysis" Bonham, N., Kasprzyk, J., Zagona, E., (2024) “Taxonomy of purposes, methods, and ...