engleski

Convergence and accuracy of numerical models using dynamic analogies

This paper describes a general procedure for proving the convergence and for the estimation of the numerical solution error of boundary problems based on the transformation of the discrete boundary problem into an equivalent discrete dynamic problem. The convergence and accuracy of numerical solutions depend on the convergence of dynamic eigenproblem spectrum. The convergence obtained in this way is valid irrespective of the applied load. The developed procedure is relatively simple, easy to perform and it guarantees the upper bounds of the error for determined discretization. The procedure can be applied for linear and non-linear boundary problems. The algorithm for solving the eigenproblem has to be able to determine the number of eigenvalues and eigenvectors sufficient to estimate the error reliably and accurately. Several examples of boundary problems used to prove the liaison in this paper are taken from the linear and nonlinear structural analyses. The applied numerical method is the finite element method, although any numerical method can be used.

convergence; accuracy; error analysis; numerical models; dynamic analogies; eigenproblem

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