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 2024 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.

 

Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem
HTML articles powered by AMS MathViewer

by Christoph Lehrenfeld, Tim van Beeck and Igor Voulis;
Math. Comp. 94 (2025), 1667-1699
DOI: https://doi.org/10.1090/mcom/4027
Published electronically: October 30, 2024

Abstract:

In this paper we present a new $H(\operatorname {div})$-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is to formulate the divergence-constraint on the active mesh, instead of the physical domain, in order to obtain robustness with respect to cut configurations without the need for a stabilization that pollutes the mass balance. This change in the formulation results in a slight inconsistency, but does not affect the accuracy of the flux variable. By applying post-processings for the scalar variable, in virtue of classical local post-processings in body-fitted methods, we retain optimal convergence rates for both variables and even the superconvergence after post-processing of the scalar variable. We present the method and perform a rigorous a priori error analysis of the method and discuss several variants and extensions. Numerical experiments confirm the theoretical results.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2020): 65N12, 65N30, 65N85
  • Retrieve articles in all journals with MSC (2020): 65N12, 65N30, 65N85
Bibliographic Information
  • Christoph Lehrenfeld
  • Affiliation: Institute for Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany
  • MR Author ID: 984763
  • ORCID: 0000-0003-0170-8468
  • Email: lehrenfeld@math.uni-goettingen.de
  • Tim van Beeck
  • Affiliation: Institute for Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany
  • ORCID: 0009-0002-4550-8636
  • Email: t.beeck@math.uni-goettingen.de
  • Igor Voulis
  • Affiliation: Institute for Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany
  • MR Author ID: 1305472
  • Email: i.voulis@math.uni-goettingen.de
  • Received by editor(s): June 22, 2023
  • Received by editor(s) in revised form: April 5, 2024, and July 10, 2024
  • Published electronically: October 30, 2024
  • © Copyright 2024 by the authors
  • Journal: Math. Comp. 94 (2025), 1667-1699
  • MSC (2020): Primary 65N12, 65N30; Secondary 65N85
  • DOI: https://doi.org/10.1090/mcom/4027
  • MathSciNet review: 4888019