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 ...

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 ...

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 ...

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

SIAM Journal on Numerical Analysis, Vol. 53, No. 3 (2015), pp. 1585-1607 (23 pages) The diffraction grating problem is modeled by a boundary value problem governed by ...

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 ...