The group is dedicated to research in numerical analysis, optimization, and mathematical applications. Its core research areas include mathematical modelling, numerical methods for partial, ordinary, and fractional differential equations (PDEs, ODEs, and FDEs), optimization and machine learning techniques for numerical simulation. The group promotes interdisciplinary research, actively engaging with the Portuguese Network for Mathematics for Industry and Innovation (PT-MATH-IN) and the Laboratory for Computational Mathematics (LCM). These collaborations foster close interaction with researchers from diverse scientific domains and with industrial partners.

The research group is strongly committed to advanced training. It is deeply involved in the supervision and training of PhD students in computational mathematics, with particular emphasis on partial differential equations, numerical linear algebra, optimization, and numerical methods for PDEs. It also supports the education of postgraduate students within the framework of the European Consortium for Mathematics in Industry (ECMI), offering a certified specialization in applied analysis and computation.