A new numerical analysis for partial differential equations with noise. This project aims to design novel numerical methods, grounded in rigorous mathematical foundations, for partial differential equations with stochastic source terms, such as for instance those modelling fluid flows with random perturbations. To ensure the accuracy of numerical simulations, preserving certain quantities of importance (mass, flux) is critical. The project's goal is to develop finite volume and high-order numeri ....A new numerical analysis for partial differential equations with noise. This project aims to design novel numerical methods, grounded in rigorous mathematical foundations, for partial differential equations with stochastic source terms, such as for instance those modelling fluid flows with random perturbations. To ensure the accuracy of numerical simulations, preserving certain quantities of importance (mass, flux) is critical. The project's goal is to develop finite volume and high-order numerical methods that are applicable in real-world settings, designed to achieve this preservation of essential quantities, and mathematically proven to be robust. The expected benefits are cost-efficient and reliable numerical tools for the scientific simulation of phenomena subjected to uncontrolled influence.Read moreRead less
Discrete functional analysis: Bridging pure and numerical mathematics. This project aims to create the first numerical analysis tools to design robust, mathematically proven algorithms for engineering problems in underground flows. These equations are essential to accurately model and understand phenomena such as oil extraction, carbon sequestration and groundwater contamination. The project will provide powerful mathematical tools to improve the reliability of numerical simulations for such cha ....Discrete functional analysis: Bridging pure and numerical mathematics. This project aims to create the first numerical analysis tools to design robust, mathematically proven algorithms for engineering problems in underground flows. These equations are essential to accurately model and understand phenomena such as oil extraction, carbon sequestration and groundwater contamination. The project will provide powerful mathematical tools to improve the reliability of numerical simulations for such challenges and significantly improve the reliability of the predictions under assumptions that are compatible with field applications.Read moreRead less