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In the last fifty years computer simulations have increased their impact on research, design, production and are now an indispensable tool for development and innovation in science and technology. Partial Differential Equations (PDEs) offer a broad and flexible framework for modeling and analyzing a number of phenomena arising in fields as diverse as physics, engineering, biology, and medicine. Not surprisingly, research on methods to simulate PDEs has a central role in modern science. IMATI has a long tradition in the study of PDEs that we address from different points of view: theoretical (existence, uniqueness and regularity of the solutions), numerical (approximation schemes, stability and adaptivity) and computational (algorithms and computing methodologies). The results of these research programs are widely used to deal with problems raising from applications as, for instance, conservation laws, fluid dynamics, electromagnetics, semiconductor devices, non linear elastic and elasto-plastic materials, including shape memory alloys and rubber models. The research on numerical and theoretical aspects of PDEs (8 researchers) is the trademark of the institute with, in the last five years, two ERC Starting grants (BioSMA and GeoPDEs) and several recognitions as plenary talks, prizes, and an impressive publication record - about 90 publications (of which 5 highly cited papers), more than 400 cites. The group constantly attracts brilliant young researchers and visiting scholars. Our research is currently developed following four main research axes: 

 

   DISCRETIZATION METHODS BASED ON THE USE OF SPLINES            DISCRETIZATION METHODS for PDEs ON POLYGONAL and POLYHEDRAL MESHES 
             
   NON CONFORMING DOMAIN DECOMPOSITION METHODS           SYSTEMS OF CONSERVATION LAWS AND RELATED TOPICS

 


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