Chapter

The Finite-Element Method

Heiner Igel

in Computational Seismology

Published in print November 2016 | ISBN: 9780198717409
Published online January 2017 | e-ISBN: 9780191835070 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198717409.003.0006
The Finite-Element Method

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The finite-element method is introduced first for the static elastic problem. The weak form of the wave equation and the Galerkin principle are discussed with linear basis functions. The solution for the static elastic problem is compared with the finite-difference-based relaxation method. The characteristic mass and stiffness matrices are introduced. The time-dependent elastic wave equation is solved using linear basis functions and simulation examples are given. The derivation of high-order shape functions (rectangular, triangular) is presented.

Keywords: finite elements; linear basis functions; Galerkin principle; mass matrix; stiffness matrix; shape functions; static elasticity

Chapter.  11567 words.  Illustrated.

Subjects: Physics

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