Numerical analysis for full and reduced order methods for the efficient and accurate solution of complex systems held by partial differential equations

The objective of this research proposal is to design and analyse innovative numerical methods for the approximation of partial differential equations (PDEs) in computational sciences and engineering. The increasing complexity of realistic models and the evolution of the computational platforms and architectures are challenging the numerical analysis community to develop more efficient, effective, and innovative methods. Our research units in SISSA, CNR, Pavia, Milano, Torino and Trento share a consolidated expertise on advanced discretisation schemes based on variational approaches, such as conforming and nonconforming finite elements (FEM), spectral and hp type finite elements (hp-FEM), immersed methods, finite volumes. Reduced order methods which rely on these schemes are considered as well. We also focus on full and reduced order methods to study how the possible uncertain/incomplete knowledge of the parameters of the PDEs, due e.g. to intrinsic variability or measurement errors, affects the outcomes of the computations.