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Springer Handbook of Materials Measurement Methods pp 973–1000Cite as

Finite Element and Finite Difference Methods

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Abstract

Finite element methods (FEM) and finite difference methods (FDM) are numerical procedures for obtaining approximated solutions to boundary-value or initial-value problems. They can be applied to various areas of materials measurement and testing, especially for the characterization of mechanically or thermally loaded specimens or components. (Experimental methods for these fields have been treated in Chapts. 7 and 8.)

The principle is to replace an entire continuous domain of a body of interest by a number of subdomains in which the unknown function is represented by simple interpolation functions with unknown coefficients. Thus, the original boundary-value problem with an infinite number of degrees of freedom is converted into a problem with a finite number of degrees of freedom approximately.

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Abbreviations

BB:

Ladyzhenskaya–Babuska–Brezzi condition

BEM:

Boundary Element Method

Bi-CGSTAB:

biconjugate gradient stabilized method

CFL:

Courant–Friedrichs–Lewy condition

CG:

conjugate gradient method

CIP:

constrained interpolated profile method

DEM:

discrete element method

FD:

finite differences

FDM:

finite difference methods

FE:

finite elements

FEA:

finite element analysis

FEM:

finite element method

FVM:

finite volume method

GLS:

Galerkin/least squares scheme

GMRES:

generalized minimal residual

QMR:

quasiminimal residual method

SOR:

successive overrelaxation

SPH:

smooth particle hydrodynamics method

SUPG:

streamline-upwind Petrov–Galerkin method

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Author information

Authors and Affiliations

  1. Advanced Manufacturing Research Institute, National Institute of Advanced Industrial Science and Technology, AIST Tsukuba East, 305-8564, Tsukuba, Japan

    Akira Tezuka Dr.

Authors
  1. Akira Tezuka Dr.
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Correspondence to Akira Tezuka Dr. .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Precision Engineering, University of Applied Sciences, TFH Berlin, Luxemburger Strasse 10, 13353, Berlin, Germany

    Horst Czichos Prof.

  2. National Institute for Materials Science (NIMS), Tsukuba, Ibaraki, Japan

    Tetsuya Saito

  3. National Institute of Standards and Technology (NIST), Gaithersburg, MD, US

    Leslie Smith

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© 2006 Springer-Verlag

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Tezuka, A. (2006). Finite Element and Finite Difference Methods. In: Czichos, H., Saito, T., Smith, L. (eds) Springer Handbook of Materials Measurement Methods. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30300-8_19

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