Error estimation for proper generalized decomposition solutions: A dual approach. (4th August 2020)

• Record Type: Journal Article
• Authors: Reis, Jonatha; Moitinho de Almeida, J. P.; Díez, Pedro; Zlotnik, Sergio
• Other Names: Giacomini Matteo guestEditor.; Veroy Karen guestEditor.; Díez Pedro guestEditor.
• Is Part Of: International journal for numerical methods in engineering. Volume 121:Number 23(2020)
• Page Start: 5275
• Page End: 5294
• Publication Date: 2020-08-04
• Subjects: equilibrium formulation -- error bounds -- error estimation -- model reduction -- proper generalized decomposition; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6452
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: 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.