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

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 ...

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.