Application of spectral element method in fluid dynamics

This work presents application of spectral element method (SEM) for solving partial differential equations. This method can be seen as combination of spectral method (SM) and finite element method (FEM). Computational domain is decomposed to smaller elements, what enable description of more general geometries. On each element is then used the spectral method, which brings high accuracy. In this work the basic theory is presented for SM and SEM with emphasize to facilitate application of this method in developing computer programs. Numerical scheme is presented on several appropriate examples. The result of this work is in comparison of solution of chosen problems obtained by SM and SEM from written program. Comparison with professional software is also done and shows power of spectral methods