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2017 | OriginalPaper | Chapter

6. Solving Phase-Field Equations with Finite Elements

Author : S. Bulent Biner

Published in: Programming Phase-Field Modeling

Publisher: Springer International Publishing

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Abstract

The finite element method, FEM, and sometimes also called finite element analysis, FEA, was originally developed in the aircraft industry in 1960s [1, 2]. Therefore, it is a very mature algorithm and widely used in engineering and science as a general numerical approach for the solution of PDEs subject to known boundary and initial conditions. The use of piecewise continuous functions over subregions of domain to approximate the unknown function was first introduced by Courant [3]. This approach was later formalized [4, 5] and term finite elements for these subregions was introduced by Clough [6]. Therefore, similar to finite difference technique the FEM is also local in nature. However, FEM has superior and unique characteristics to describe very complex geometries and boundaries of domains. There are plenty of textbook and online materials covering both theoretical and practical aspects of FEM or FEA and some of them are listed in the reference section.
Metadata
Title
Solving Phase-Field Equations with Finite Elements
Author
S. Bulent Biner
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-41196-5_6

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