Division of Computational Mathematics
Department of Mathematics
During the last decade, stable high order finite difference methods and finite volume methods applied to initial-boundary-value-problems have been developed. The stability is due to the use of so-called summation-by-parts operators, penalty techniques for implementing boundary and interface conditions, and the energy method for proving stability. In this talk we discuss new aspects of this technique including the relation to the initial-boundary-value-problem. By reusing the main ideas behind the development, new time-integration procedures, boundary conditions, boundary procedures, multi-physics couplings and uncertainty quantification, have been derived. We will present the theory by analyzing simple examples and apply to very complex problems.