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 ...

In this paper, we perform an a posteriori error analysis of a multiscale operator decomposition finite element method for the solution of a system of coupled elliptic ...

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