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 ...

Sebastian Reich, Backward Error Analysis for Numerical Integrators, SIAM Journal on Numerical Analysis, Vol. 36, No. 5 (Jul. - Sep., 1999), pp. 1549-1570 ...

This paper provides an error analysis for the Crank-Nicolson method of time discretization applied to spatially discrete Galerkin approximations of the nonstationary Navier-Stokes equations.

Numerical Solution of Systems of Linear Equations, Iterative Methods Formulation and analysis of basic stationary methods e.g. Gauss-Jacobi, Gauss-Seidel. The numerical solution of Poisson's equation.

In numerical analysis, we focus on developing and analysing advanced discretization schemes, including their stability and convergence properties, using, e.g., tools from functional analysis.