Finite Element Methods with Higher Order Polynomials

摘要: The Finite Element Method (FEM) has recently been implemented in the fluid mechanics field to solve the instabilities that arise as a result of the equations’ non-linearities. For this reason, novel formulations of FEM were introduced, including the use of orthogonal polynomials and high-order polynomials. In this review, the focus rests on studying and analysing the aforementioned formulations and describing their improvements over the classical method. Initially, a theoretical background of FEM is introduced, with an emphasis on evaluating the basis of the function space. Additionally, the p-version of FEM is analysed, using Legendre polynomials. A comparison of the classical h-version and the p-version in terms of convergence. Moreover, other formulations that yield, using higher-order polynomials, such as hp-FEM and Spectral Element Method, are briefly reviewed. Finally, applications on FEM are presented …