The simulation of multidisciplinary applications use very often a combination of heterogeneous and disjoint numerical techniques that are hard to put together by the user, and whose mathematical foundation is obscure. An example of this situation is the numerical modeling of the physical processes taking place in nuclear fusion reactors. This problem, which can be modeled by a set of partial differential equations, is extremely challenging. It involves (essentially) fluid mechanics, electromagnetics, thermal radiation and neutronics. The most common numerical approaches to each of these problems separately are very different and their coupling is a hard and inefficient task.Our main objective in this proposal is to develop and analyze a unified numerical framework based on stabilized finite element methods based on multi-scale decompositions capable to simulate all the physical processes taking place in nuclear fusion technology. The project aims at giving a substantial contribution to the numerical approximation of every physical process as well as efficient coupling techniques for the multiphysics problems.The development of the numerical formulations we propose and their application require mastering different physics, designing numerical approximations for these different physical problems, analyzing mathematically the resulting methods, implementing them in an efficient way in parallel platforms and understanding the results and drawing conclusions, both from a physical and from an engineering perspective. Advanced research in physical modeling, numerical approximations, mathematical analysis and computer implementation are the keys to meeting these objectives.The successful implementation of the project will provide advanced numerical techniques for the simulation of the processes taking place in a fusion reactor. A deliverable product of the project will be a unified finite element software package that will be an extremely valuable tool.