Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Error estimates for discrete generalized FEMs with locally optimal spectral approximations
HTML articles powered by AMS MathViewer

by Chupeng Ma and Robert Scheichl HTML | PDF
Math. Comp. 91 (2022), 2539-2569 Request permission

Abstract:

This paper is concerned with error estimates of the fully discrete generalized finite element method (GFEM) with optimal local approximation spaces for solving elliptic problems with heterogeneous coefficients. The local approximation spaces are constructed using eigenvectors of local eigenvalue problems solved by the finite element method on some sufficiently fine mesh with mesh size $h$. The error bound of the discrete GFEM approximation is proved to converge as $h\rightarrow 0$ towards that of the continuous GFEM approximation, which was shown to decay nearly exponentially in previous works. Moreover, even for fixed mesh size $h$, a nearly exponential rate of convergence of the local approximation errors with respect to the dimension of the local spaces is established. An efficient and accurate method for solving the discrete eigenvalue problems is proposed by incorporating the discrete $A$-harmonic constraint directly into the eigensolver. Numerical experiments are carried out to confirm the theoretical results and to demonstrate the effectiveness of the method.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2020): 65M60, 65N15
  • Retrieve articles in all journals with MSC (2020): 65M60, 65N15
Additional Information
  • Chupeng Ma
  • Affiliation: Institute of Scientific Research, Great Bay University, Songshan Lake International Innovation Entrepreneurship Community A5, Dongguan 523000, China
  • MR Author ID: 1251608
  • Email: chupeng.ma@gbu.edu.cn
  • Robert Scheichl
  • Affiliation: Institute for Applied Mathematics and Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, Heidelberg 69120, Germany
  • MR Author ID: 661163
  • ORCID: 0000-0001-8493-4393
  • Email: r.scheichl@uni-heidelberg.de
  • Received by editor(s): September 23, 2021
  • Received by editor(s) in revised form: March 21, 2022, and April 28, 2022
  • Published electronically: July 12, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2539-2569
  • MSC (2020): Primary 65M60; Secondary 65N15
  • DOI: https://doi.org/10.1090/mcom/3755
  • MathSciNet review: 4473096