Skip to Main Content

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.

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.


Weak discrete maximum principle of finite element methods in convex polyhedra
HTML articles powered by AMS MathViewer

by Dmitriy Leykekhman and Buyang Li HTML | PDF
Math. Comp. 90 (2021), 1-18 Request permission


We prove that the Galerkin finite element solution $u_h$ of the Laplace equation in a convex polyhedron $\varOmega$, with a quasi-uniform tetrahedral partition of the domain and with finite elements of polynomial degree $r\geqslant 1$, satisfies the following weak maximum principle: \begin{align*} \left \|u_{h}\right \|_{L^{\infty }(\varOmega )} \leqslant C\left \|u_{h}\right \|_{L^{\infty }(\partial \varOmega )} , \end{align*} with a constant $C$ independent of the mesh size $h$. By using this result, we show that the Ritz projection operator $R_h$ is stable in $L^\infty$ norm uniformly in $h$ for $r\geq 2$, i.e., \begin{align*} \|R_hu\|_{L^{\infty }(\varOmega )} \leqslant C\|u\|_{L^{\infty }(\varOmega )} . \end{align*} Thus we remove a logarithmic factor appearing in the previous results for convex polyhedral domains.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 65N12, 65N30
  • Retrieve articles in all journals with MSC (2010): 65N12, 65N30
Additional Information
  • Dmitriy Leykekhman
  • Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
  • MR Author ID: 680657
  • Email:
  • Buyang Li
  • Affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
  • MR Author ID: 910552
  • Email:
  • Received by editor(s): September 18, 2019
  • Received by editor(s) in revised form: February 29, 2020, and April 13, 2020
  • Published electronically: July 27, 2020
  • Additional Notes: This work was partially supported by NSF DMS-1913133 and a Hong Kong RGC grant (project no. 15300519).
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 1-18
  • MSC (2010): Primary 65N12, 65N30
  • DOI:
  • MathSciNet review: 4166450