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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.

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 of a regularized finite element discretization of the two-dimensional Monge–Ampère equation
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by Dietmar Gallistl and Ngoc Tien Tran HTML | PDF
Math. Comp. 92 (2023), 1467-1490 Request permission


This paper proposes a regularization of the Monge–Ampère equation in planar convex domains through uniformly elliptic Hamilton–Jacobi–Bellman equations. The regularized problem possesses a unique strong solution $u_\varepsilon$ and is accessible to the discretization with finite elements. This work establishes uniform convergence of $u_\varepsilon$ to the convex Alexandrov solution $u$ to the Monge–Ampère equation as the regularization parameter $\varepsilon$ approaches $0$. A mixed finite element method for the approximation of $u_\varepsilon$ is proposed, and the regularized finite element scheme is shown to be uniformly convergent. The class of admissible right-hand sides are the functions that can be approximated from below by positive continuous functions in the $L^1$ norm. Numerical experiments provide empirical evidence for the efficient approximation of singular solutions $u$.
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Additional Information
  • Dietmar Gallistl
  • Affiliation: Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
  • MR Author ID: 1020312
  • Email:
  • Ngoc Tien Tran
  • Affiliation: Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
  • MR Author ID: 1437571
  • Email:
  • Received by editor(s): December 20, 2021
  • Received by editor(s) in revised form: June 7, 2022, July 26, 2022, and September 11, 2022
  • Published electronically: February 6, 2023
  • Additional Notes: This project received funding from the European Union’s Horizon 2020 research and innovation programme (project DAFNE, grant agreement No. 891734).
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 1467-1490
  • MSC (2020): Primary 35J96, 65N12, 65N30, 65Y20
  • DOI:
  • MathSciNet review: 4570330