Paper Info
Title
Quasi-Optimal Mesh Sequence Construction Through Smoothed Adaptive Finite Element Methods
Abstract
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.
Year
DOI
Venue
2021
10.1137/19M1262097
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
DocType
Volume
adaptive mesh refinement, finite element method, second-order elliptic PDEs, a posteriori error analysis, inexact algebraic solution, iterative solvers, smoothing iterations, grid construction
Journal
43
Issue
ISSN
Citations 
3
1064-8275
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Ornela Mulita100.34
Stefano Giani2369.55
Luca Heltai3719.51