Finite Element Methods with Higher Order Polynomials

Konstantina C. Kyriakoudi () and Michail A. Xenos ()
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Konstantina C. Kyriakoudi: University of Ioannina
Michail A. Xenos: University of Ioannina

A chapter in Exploring Mathematical Analysis, Approximation Theory, and Optimization, 2023, pp 161-176 from Springer

Abstract: Abstract 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, revealing the effects of the increase in the degree of the polynomials when solving a fluid mechanics problem.

Keywords: Finite element method; p-Version; Adaptive; Fluid mechanics; 65N30; 65M60; 76M10 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-46487-4_10

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DOI: 10.1007/978-3-031-46487-4_10

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