Error estimation for proper generalized decomposition solutions: A dual approach
Author (s): Reis, J.; Moitinho de Almeida, J.P.; Díez, P. and Zlotnik, S.Journal: International Journal for Numerical Methods in Engineering
Volume: 121 (23)
Pages: 5275 - 5294
Date: 2020
Abstract:
The proper generalized decomposition is a well-established reduced order method, used to efficiently obtain approximate solutions of multi-dimensional problems in a procedure that controls the effects of the “curse of dimensionality.” The question of assessing the quality of the solutions obtained and adapting the approximations assumed, for example, the finite element meshes used, so that the best result is obtained at minimal cost, remains a relevant challenge. This article deals with finite element solutions for solid mechanics problems, using the error obtained from a dual analysis, the difference between complementary solutions, to bound the error in the solutions and to drive an optimal adaptivity process, which obtains meshes with errors significantly lower than those obtained using a uniform refinement.
Bibtex:
@article{2020-IJNME-RMDZ, Author = {Reis, Jonatha and Moitinho de Almeida, Jose Paulo and D{\'i}ez, Pedro and Zlotnik, Sergio}, Title = {Error estimation for proper generalized decomposition solutions: A dual approach}, Fjournal = {International Journal for Numerical Methods in Engineering}, Volume = {121}, Number = {23}, Pages = {5275-5294}, Year = {2020}, Doi = {10.1002/nme.6452}, }