Impact Factor: 3.8

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Journal of Numerical Mathematics

Editor-in-Chief: Maxim Olshanskiy
Managing Editor: Andrea Bonito

Language: English

First published: March 1, 2001

Publication Frequency: 4 issues per year

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Objective
The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.

Topics

Numerical Mathematics
Computational Mathematics
Applied Mathematics
Numerical Linear Algebra
Numerical Analysis
Optimal Control/Optimization
Scientific Computing
Computational Fluid Dynamics
Finance
Life Sciences

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Adaptive computation of elliptic eigenvalue topology optimization with a phase-field approach

February 27, 2025

Jing Li, Yifeng Xu, Shengfeng Zhu

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In this paper, we study adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two-dimensional numerical examples for illustration of efficiency and accuracy. Theoretical findings consist in the vanishing limit of a subsequence of estimators and the convergence of the relevant subsequence of adaptively-generated solutions to a solution to the continuous optimality system.
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Long time behavior of the field–road diffusion model: an entropy method and a finite volume scheme

February 26, 2025

Matthieu Alfaro, Claire Chainais-Hillairet

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We consider the so-called field–road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions (a field and a road in a population dynamics context) and coupled through exchange terms on the road, which makes its analysis quite involved. We propose a two-point flux approximation (TPFA) finite volume scheme. In both the continuous and the discrete settings, we prove the dissipation of a quadratic entropy, with some entropy dissipation-entropy relation, leading to the exponential decay in time of the solution towards the stationary state selected by the total mass of the initial data. To deal with the problem of different dimensions in the proof of the entropy dissipation-entropy relation, we artificially “thicken” the road and adapt the proof of the Poincaré–Wirtinger inequality. Numerical simulations confirm and complete the analysis, and raise new issues.
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A medius error analysis for the conforming discontinuous Galerkin finite element methods

February 24, 2025

Yuping Zeng, Shangyou Zhang

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In this paper, we derive an improved error estimate of a conforming discontinuous Galerkin (CDG) method for both second and fourth order elliptic problems, assuming only minimal regularity on the exact solutions. The result we established is called a medius error estimate since it relies on both a priori and a posteriori analysis. Compared with the standard interior penalty discontinuous Galerkin (IPDG) method, when choosing the standard DG norm, an additional term ‖∇ u − ∇ w v h ‖ 0 is incorporated in the CDG formulation for second order elliptic equation, while for the case of fourth order equation, this term becomes ‖ Δ u − Δ w v h ‖ 0 ${\Vert}{\Delta}\mathbb{u}-{{\Delta}}_{w}{\mathbb{v}}_{h}{{\Vert}}_{0}$ . These terms disappear if we directly analyze the nonstandard error formulations ‖∇ u − ∇ w u h ‖ 0 and ‖ Δ u − Δ w u h ‖ 0 ${\Vert}{\Delta}\mathbb{u}-{{\Delta}}_{w}{\mathbb{u}}_{h}{{\Vert}}_{0}$ . Extensive numerical results are also carried out to validate our theoretical findings.
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Error analysis of virtual element method for the Poisson–Boltzmann equation

February 24, 2025

Linghan Huang, Shi Shu, Ying Yang

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The Poisson–Boltzmann equation, which incorporates the source of the Dirac distribution, has been widely applied in predicting the electrostatic potential of biomolecular systems in solution. In this paper we discuss and analyse the virtual element method for the Poisson–Boltzmann equation on general polyhedral meshes. Nearly optimal error estimates, approaching the best possible accuracy, are achieved for the virtual element approximation in both the L 2 -norm and H 1 -norm, even when the solution of the entire domain has low regularity. The efficiency of the virtual element method and the validity of the proposed theoretical prediction are confirmed through numerical experiments conducted on various polyhedral meshes.
Open Access
A Robin–Robin strongly coupled partitioned method for fluid–poroelastic structure interaction

February 24, 2025

Connor Parrow, Martina Bukač

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This work focuses on the development of a novel, strongly-coupled, second-order partitioned method for fluid–poroelastic structure interaction. The flow is assumed to be viscous and incompressible, and the poroelastic material is described using the Biot model. To solve this problem, a numerical method is proposed, based on Robin interface conditions combined with the refactorization of the Cauchy’s one-legged ‘ ϑ -like’ method. This approach allows the use of the mixed formulation for the Biot model. The proposed algorithm consists of solving a sequence of Backward Euler–Forward Euler steps. In the Backward Euler step, the fluid and poroelastic structure problems are solved iteratively until convergence. Then, the Forward Euler problems are solved using equivalent linear extrapolations. We prove that the iterative procedure in the Backward Euler step is convergent, and that the converged method is stable when ϑ ∈ [1/2, 1]. Numerical examples are used to explore convergence rates with varying parameters used in our scheme, and to compare our method to a monolithic method based on Nitsche’s coupling approach.
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A subspace framework for L _∞ model reduction

January 15, 2025

Emre Mengi

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We propose an approach for the L ∞ ${\mathcal{L}}_{\infty }$ model reduction of descriptor systems based on the minimization of the L ∞ ${\mathcal{L}}_{\infty }$ objective by means of smooth optimization techniques. Direct applications of smooth optimization techniques are not feasible even for systems of modest order, since the optimization techniques converge at best at a linear rate requiring too many evaluations of the costly L ∞ ${\mathcal{L}}_{\infty }$ -norm objective to be practical. We replace the original system with a system of smaller order interpolating the original system at points on the imaginary axis, minimize the L ∞ ${\mathcal{L}}_{\infty }$ objective after this replacement, and refine the smaller system based on the minimization. We also describe how asymptotic stability constraints on the reduced system sought can be incorporated into our approach. The numerical experiments illustrate that the approach leads to locally optimal solutions to the L ∞ ${\mathcal{L}}_{\infty }$ model reduction problem, and its capability to deal with systems of order a few ten thousands.
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Stability and error analysis of a semi-implicit scheme for incompressible flows with variable density and viscosity

November 4, 2024

An Vu, Loic Cappanera

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We study the stability and convergence properties of a semi-implicit time stepping scheme for the incompressible Navier–Stokes equations with variable density and viscosity. The density is assumed to be approximated in a way that conserves the minimum-maximum principle. The scheme uses a fractional time-stepping method and the momentum, which is equal to the product of the density and velocity, as a primary unknown. The semi-implicit algorithm for the coupled momentum-pressure is shown to be conditionally stable and the velocity is shown to converge in L 2 norm with order one in time. Numerical illustrations confirm that the algorithm is stable and convergent under classic CFL condition even for sharp density profiles.
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Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs

November 4, 2024

Philipp Bringmann, Maximilian Brunner, Dirk Praetorius, Julian Streitberger

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We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest G ( u ⋆ ) with a linear goal functional G and the solution u ⋆ to a general second-order nonsymmetric linear elliptic partial differential equation. The current state of the analysis of iterative algebraic solvers for nonsymmetric systems lacks the contraction property in the norms that are prescribed by the functional analytic setting. This seemingly prevents their application in the optimality analysis of goal-oriented adaptivity. As a remedy, this paper proposes a goal-oriented adaptive iteratively symmetrized finite element method (GOAISFEM). It employs a nested loop with a contractive symmetrization procedure, e.g., the Zarantonello iteration, and a contractive algebraic solver, e.g., an optimal multigrid solver. The various iterative procedures require well-designed stopping criteria such that the adaptive algorithm can effectively steer the local mesh refinement and the computation of the inexact discrete approximations. The main results consist of full linear convergence of the proposed adaptive algorithm and the proof of optimal convergence rates with respect to both degrees of freedom and total computational cost (i.e., optimal complexity). Numerical experiments confirm the theoretical results and investigate the selection of the parameters.
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Effective highly accurate time integrators for linear Klein–Gordon equations across the scales

September 11, 2024

Karolina Kropielnicka, Karolina Lademann, Katharina Schratz

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We propose an efficient approach for time integration of Klein–Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant does not grow as the oscillations increase. Numerical experiments highlight our theoretical findings and demonstrate the efficiency of the new schemes.

Journal Impact Factor	3.8	2023, Journal Citation Reports (Clarivate, 2024)
5-year Journal Impact Factor	3.0	2023, Journal Citation Reports (Clarivate, 2024)
Journal Citation Indicator	2.41	2023, Journal Citation Reports (Clarivate, 2024)
CiteScore	5.9	2023, Scopus (Elsevier B.V., 2024)
SCImago Journal Rank	1.892	2023, SJR (Scimago Lab, 2024; Data Source: Scopus)
Source Normalized Impact per Paper	2.237	2023, CWTS Journal Indicators (CWTS B.V., 2024; Data Source: Scopus)
Mathematical Citation Quotient	1.75

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References should be collected at the end of the paper, numbered with Arabic numerals in alphabetical order of the authors' names and surrounded by square brackets. Please use abbreviations for titles of journals in accordance with those listed in Mathematical Reviews.
o Articles in journals:　
[1] A. Carbonaro, G. Metafune and C. Spina, Parabolic Schrödinger operators, J. Math
Anal. and Appl. 343 (2008), 965-974.
o Articles ahead of print:　
[2] D. Farley and L. Sabalka, Presentations of graph braid groups, Forum Math. (2010), doi: 10.1515/FORM.2011.086.
o Books and Monographs:　
[3] I. M. Isaacs, Character theory of finite groups, AMS Chelsea Publishing, 2006.
o Chapters:　
[4] T. De Medts, F. Haot, R. Knop and H. Van Maldeghem, On the uniqueness of the unipotent subgroups of some Moufang sets, in: Finite Geometries, Groups, and Computation, pp. 43-66, de Gruyter, Berlin, 2006.

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Editor-in-Chief
Maxim Olshanskii, Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA
[email protected]

Managing Editor
Andrea Bonito, Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
[email protected]

Editorial Advisory Board

Markus Bachmayr, Institut für Geometrie und Praktische Mathematik
Michele Benzi, Scuola Normale Superiore di Pisa
Susanne Brenner, Louisiana State University
Erik Burman, University College London
Carsten Carstensen, Humboldt University of Berlin
Miloslav Feistauer, Charles University in Prague
Simon Foucart, Texas A&M University
Jean-Luc Guermond, Texas A&M University
Johnny Guzman, Brown University
Daniel Kressner, EPFL
Christoph Lehrenfeld, University of Gottingen
Frédéric Nataf, Sorbonne University
Michael Neilan, University of Pittsburgh
Fabio Nobile, EPFL
Alfio Quarteroni, Politecnico di Milan
Leo Rebholz, Clemson University
Sergey Repin, Russian Academy of Science
Arnold Reusken, RWTH Aachen University
Valeria Simoncini, University of Bologna
Martin Stoll, TU Chemnitz
Eugene Tyrtyshnikov, Russian Academy of Science
Stefan Volkwein, University of Konstanz
Shawn Walker, Louisiana State University
Jun Zou, The Chinese University of Hong Kong

Honorary Members
Raytcho Lazarov, Texas A&M University
Pekka Neittaanmäki, University of Jyväskylä
Olivier Pironneau, French Academy of Sciences
Rolf Rannacher, Heidelberg University

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Additional information

Online ISSN:

1569-3953

Print ISSN:

1570-2820

Language:

English

Publisher:

De Gruyter

Additional information

First published:

March 1, 2001

Publication Frequency:

4 issues per year

Audience(s) for this journal

Researchers and practitioners of all disciplines related to Numerical Mathematics

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