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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Multilevel methods for nonuniformly elliptic operators and fractional diffusion
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by Long Chen, Ricardo H. Nochetto, Enrique Otárola and Abner J. Salgado PDF
Math. Comp. 85 (2016), 2583-2607 Request permission


We develop and analyze multilevel methods for nonuniformly elliptic operators whose ellipticity holds in a weighted Sobolev space with an $A_2$–Muckenhoupt weight. Using the so-called Xu-Zikatanov (XZ) identity, we derive a nearly uniform convergence result under the assumption that the underlying mesh is quasi-uniform. As an application we also consider the so-called $\alpha$-harmonic extension to localize fractional powers of elliptic operators. Motivated by the scheme proposed by the second, third and fourth authors, we present a multilevel method with line smoothers and obtain a nearly uniform convergence result on anisotropic meshes. Numerical experiments illustrate the performance of our method.
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Additional Information
  • Long Chen
  • Affiliation: Department of Mathematics, University of California at Irvine, Irvine, California 92697
  • MR Author ID: 735779
  • Email:
  • Ricardo H. Nochetto
  • Affiliation: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 131850
  • Email:
  • Enrique Otárola
  • Affiliation: Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile
  • Email:
  • Abner J. Salgado
  • Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
  • MR Author ID: 847180
  • Email:
  • Received by editor(s): March 17, 2014
  • Received by editor(s) in revised form: April 25, 2015
  • Published electronically: March 3, 2016
  • Additional Notes: The first author has been supported by NSF grants DMS-1115961, DMS-1418934, and DOE prime award # DE-SC0006903.
    The second and fourth authors have been supported in part by NSF grants DMS-1109325 and DMS-1411808.
    The third author was supported in part by the NSF grants DMS-1109325 and DMS-1411808 and by CONICYT through a CONICYT-FULBRIGHT Fellowship
    The fourth author was supported by NSF grant DMS-1418784
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 2583-2607
  • MSC (2010): Primary 65N55, 65F10, 65N22, 65N30, 35S15, 65N12
  • DOI:
  • MathSciNet review: 3522963