Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

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 ...

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

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 ...

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 ...

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 ...