This project primarily focuses on development of efficient and reliable adaptive algorithms, high order stabilized finite element methods (FEMs) for computational fluid dynamics, in particular compressible flow problems. Problems in science and industry often involve complex geometries and shapes. Simulation of flows around cars, airplanes, rackets, wings, birds, and supersonic jets are real examples which can be required from the industry. Numerical methods that we develop within this project are designed to work for any complex geometry, to be highly accurate and to be applicable to the real life problems.