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

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.



        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},