The Finite Volume method, and several of its variants, is a spatial discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods are also built to preserve some properties of the continuous equations, including maximum principles, dissipativity, monotone decay of the free energy, asymptotic stability, or stationary solutions. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. In recent years, the efficient implementation of these methods in numerical software packages, more specifically to be used in supercomputers, has drawn some attention.
The main goal of the symposium is to bring together mathematicians, physicists, and engineers interested in physically motivated discretizations, and in their applications. Contributions to the further advancement of the theoretical understanding of suitable finite volume, finite element, discontinuous Galerkin and other discretization schemes, as well as the exploration of new application fields, including software-related improvements and interaction with machine learning, are also welcome.
TOPICS OF MAIN INTEREST
- Design and analysis of numerical methods
- Preservation of physical properties at the discrete level
- Convergence, stability, a priori and a posteriori error analysis
- Applications at the interface with other disciplines
- HPC, parallel computing
- Industrial applications
- Model reduction and multiscale methods
- High-order methods
- Uncertainty quantification and stochastic problems
- Numerical schemes enhanced with machine learning
- Open source software related to the above topics
This work was supported by the IdEx University of Strasbourg.