We propose a new algorithm for adaptive finite element methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the V-cycle multigrid method: we replace accurate algebraic solutions in intermediate cycles of the classical AFEM with the application of a prolongation step, followed by the application of a smoother. Even though these intermediate solutions are far from the exact algebraic solutions, their a posteriori error estimation produces a refinement pattern that is substantially equivalent to the one that would be generated by classical AFEM, at a considerable fraction of the computational cost. We provide a qualitative analysis of how the error propagates throughout the algorithm, and we present a series of numerical experiments that highlight the efficiency and the computational speedup of S-AFEM.
Quasi-optimal mesh sequence construction through smoothed adaptive finite element methods / Mulita, O.; Giani, S.; Heltai, L.. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 43:3(2021), pp. 2211-2241. [10.1137/19M1262097]
|Titolo:||Quasi-optimal mesh sequence construction through smoothed adaptive finite element methods|
|Autori:||Mulita, O.; Giani, S.; Heltai, L.|
|Data di pubblicazione:||2021|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1137/19M1262097|
|Fulltext via DOI:||http://dx.doi.org/10.1137/19M1262097|
|Appare nelle tipologie:||1.1 Journal article|