Spectral approximation of a strain-limiting nonlinear elastic model

Author: 

Gelmetti, N
Suli, E

Publication Date: 

23 December 2018

Journal: 

Matematički Vesnik

Last Updated: 

2020-05-20T12:48:39.763+01:00

Issue: 

1-2

Volume: 

71

page: 

63–89-

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.

Symplectic id: 

953063

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article