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 ...

SIAM Journal on Numerical Analysis contains research articles on the development and analysis of numerical methods including their convergence, stability, and error ...

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 ...

In this research field we are developing advanced computational methods centered around efficient solution strategies for partial differential equations. In numerical analysis, we focus on developing ...

Error estimates for fully discretized particle or simulation methods for multidimensional Vlasov-Poisson systems are provided. The treatment requires stability ...

An error analysis of approximation of deltas (derivatives of the solution to the Cauchy problem for parabolic equations) by finite differences is given, taking into ...