Research Project

Abstract: Structure-preserving numerical methods aim to preserve the geometric and physical properties of a model at a discrete level, that are not usually taken into account by traditional numerical schemes. These properties may include conservation or decaying of certain quantities of physical interest, and the preservation of the solution’s positivity in order to avoid physically meaningless negative values. The design of numerical methods provided with discrete analogues of these properties is important not just from the physical perspective, but also due to their strong influence on the stability and optimal convergence of the method, guaranteeing robustness in long time simulations.
One of the common issues of structure-preserving discretizations for nonlinear models is that they usually lead to large systems of nonlinear equations that must be solved accurately in order to preserve the discrete physical properties. In fact, there has been an apparent trade-off between the efficiency and the structure-preserving properties of numerical methods for these problems.
The main goal of this project is to design efficient structure-preserving methods for some important nonlinear models based on either time-stepping schemes or space–time discretizations.

Duration of stay: 13th March to 13th September 2023