THE OBJECTIVE OF THIS PROJECT IS TO EVALUATE HIGH ORDER FINITE ELEMENT DISCRETIZATION SCHEMES, EMPHASIZING INCREASED STABILITY, ROBUSTNESS AND EFFICIENCY. THE STABILITY AND ROBUSTNESS ISSUES CAN BE ADDRESSED BY CREATING ENTROPY STABLE DISCRETIZATION SCHEMES, WHICH IS POSSIBLE BOTH FOR THE INCOMPRESSIBLE AND COMPRESSIBLE NAVIER-STOKES EQUATIONS. BESIDES ALGORITHMIC IMPROVEMENTS, THE EFFICIENCY OF HIGH ORDER DISCRETIZATION CAN BE INCREASED BY USING GRAPHICAL PROCESSING UNITS, I.E. GPUS. HIGH ORDER DISCRETIZATION ARE COMPUTATIONALLY MUCH MORE INTENSIVE THAN THEIR LOWER ORDER COUNTERPARTS, WHICH MAKE THEM ESPECIALLY SUITED FOR GPUS. HOWEVER, STANDARD CPU BASED SYSTEMS REMAIN IMPORTANT AS WELL AND IT IS THEREFORE THE INTENTION TO DEVELOP SOFTWARE USING A PERFORMANCE PORTABLE FRAMEWORK, SUCH THAT EFFICIENT EXECUTION IS OBTAINED FOR BOTH CPUS AND GPUS.