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.


Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
HTML articles powered by AMS MathViewer

by J. M. Melenk and S. Sauter PDF
Math. Comp. 79 (2010), 1871-1914 Request permission


A rigorous convergence theory for Galerkin methods for a model Helmholtz problem in ${\mathbb {R}}^{d}$, $d \in \{1,2,3\}$ is presented. General conditions on the approximation properties of the approximation space are stated that ensure quasi-optimality of the method. As an application of the general theory, a full error analysis of the classical $hp$-version of the finite element method ($hp$-FEM) is presented for the model problem where the dependence on the mesh width $h$, the approximation order $p$, and the wave number $k$ is given explicitly. In particular, it is shown that quasi-optimality is obtained under the conditions that $kh/p$ is sufficiently small and the polynomial degree $p$ is at least $O(\log k)$.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 35J05, 65N12, 65N30
  • Retrieve articles in all journals with MSC (2010): 35J05, 65N12, 65N30
Additional Information
  • J. M. Melenk
  • Affiliation: Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
  • MR Author ID: 613978
  • ORCID: 0000-0001-9024-6028
  • Email:
  • S. Sauter
  • Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr 190, CH-8057 Zürich, Switzerland
  • MR Author ID: 313335
  • Email:
  • Received by editor(s): July 15, 2008
  • Published electronically: April 27, 2010
  • © Copyright 2010 American Mathematical Society
  • Journal: Math. Comp. 79 (2010), 1871-1914
  • MSC (2010): Primary 35J05, 65N12, 65N30
  • DOI:
  • MathSciNet review: 2684350