Spectral approximation of a strain-limiting nonlinear elastic model

Journal article

Abstract:: We construct a numerical algorithm for the approximate solution of a non-linear elastic limiting strain model based on the Fourier spectral method. The existence and uniqueness of the numerical solution are proved. Assuming that the weak solution to the boundary-value problem possesses suitable Sobolev regularity, the sequence of numerical solutions is shown to converge to the weak solution of the problem at an optimal rate. The numerical method represents a finite-dimensional system of nonlinear equations. An iterative method is proposed for the approximate solution of this system of equations and is shown to converge, at a linear rate, to the unique solution of the numerical method. The theoretical results are illustrated by numerical experiments.

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Keywords:: limiting strain models

spectral method

nonlinear elasticity

convergence
Pubs id:: pubs:953063
UUID:: uuid:9a438b36-37de-4d66-a2c3-ada9f9df2465
Local pid:: pubs:953063
Source identifiers:: 953063
Deposit date:: 2018-12-17

Copyright holder:: Gelmetti and Suli
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