ESAIM Mathematical Modelling and Numerical Analysis

About ESAIM Mathematical Modelling and Numerical Analysis

About ESAIM: Mathematical Modelling and Numerical Analysis

ESAIM: Mathematical Modelling and Numerical Analysis, universally known by its abbreviation M2AN, is a French international journal of applied mathematics published by EDP Sciences within the ESAIM family — ESAIM standing for the European Series in Applied and Industrial Mathematics, produced in association with SMAI, the French society for applied and industrial mathematics. The publisher's own one-sentence description is precise and demanding: “ESAIM: M2AN publishes original research papers in Mathematical Modelling and Numerical Analysis providing rigorous theoretical analysis and evidence of computational relevance.” Both halves of that sentence are editorial policy. A paper that models without rigorous analysis, and a paper that analyses without any evidence that the mathematics connects to computation, each fail one half of the journal's stated test.

The journal's ISSN history reflects its age and its move between publishing eras. The record assigned to this profile carries four ISSNs — 0764-583X and 1290-3841 from its earlier EDP Sciences period, and 2822-7840 and 2804-7214 from its current period. Clarivate's Web of Science Master Journal List records the journal under ISSN 2822-7840 and eISSN 2804-7214, lists its publisher as EDP Sciences at Les Ulis, France, and places it in the Science Citation Index Expanded, with additional indexing in Current Contents Physical, Chemical and Earth Sciences and Essential Science Indicators. A second record on this site, discussed at the end of this profile, carries only the two current ISSNs and an h-index of 88; the four-ISSN record and the two-ISSN record describe the same journal at different points in its identifier history, not two different journals.

Scope: Modelling With Analysis, Analysis With Computation

M2AN's territory is the mathematics of models that are computed. Its papers build, analyse and test numerical methods for problems arising in physics, engineering, fluid and solid mechanics, and the wider sciences — and, crucially, they prove things about those methods. The journal's published record illustrates the standard. A study of spectral Galerkin methods for a class of Fokker–Planck equations arising in the kinetic theory of dilute polymers, including the FENE model of polymer dynamics, develops existence of weak solutions for a degenerate problem with an unbounded drift coefficient, constructs a fully discrete spectral method, proves optimal-order convergence in a Maxwellian-weighted norm, and then illustrates the analysis with numerical experiments in two space dimensions. A paper on high-order splitting methods for nonlinear evolutionary Schrödinger equations, applied to the equations of electron dynamics, performs the error analysis of the methods and connects it to a concrete computational physics problem. A long-running line of work revisiting power-series solutions of the Euler equations for an incompressible fluid shows the journal's tolerance for depth: authors recomputed, by computer algebra, a series previously carried to 35 terms, extended it to 52 terms, and used the extended computation to challenge an earlier conclusion about blow-up — analysis and computation correcting each other in public.

From that record, the journal's expectations can be stated concretely. Manuscripts should formulate a model or method precisely, state assumptions, prove convergence, stability, error estimates or well-posedness as appropriate, and support the theory with numerical results that actually test it — convergence rates observed against rates proved, behaviour on problems with known difficulty, comparisons that illuminate rather than decorate. Purely empirical simulation studies without analysis, and purely formal theory with no computational bearing, sit outside the publisher's stated scope. Application areas visible across the journal's history include fluid dynamics, kinetic theory, continuum mechanics, electromagnetism, Schrödinger and quantum dynamics, polymer modelling and scientific computing more generally — always entered through the door of mathematical modelling and numerical analysis, not through the application alone.

The ESAIM Family and the SMAI Connection

M2AN does not stand alone. ESAIM is a family of journals associated with SMAI covering the main territories of applied mathematics: control, optimisation and calculus of variations (ESAIM: COCV); probability and statistics (ESAIM: P&S); mathematical modelling of natural phenomena (MMNP); and proceedings and surveys, alongside the RAIRO journals in operations research and theoretical informatics published in the same EDP Sciences stable. For an author, the family structure is a routing device. A paper on optimal control of a partial differential equation may belong in COCV rather than M2AN; a stochastic numerical method may sit between M2AN and P&S; a modelling paper centred on a biological phenomenon with lighter numerical analysis may fit MMNP better. Choosing the right ESAIM title first is the single most effective step an author can take, because editors assess fit against each journal's own stated sentence of scope, and M2AN's sentence insists on both rigorous analysis and computational relevance.

The family's French origin still shapes its character. M2AN grew out of the strong French school of numerical analysis — the tradition associated with the analysis of finite element methods, variational formulations and partial differential equations — and it retains a European centre of gravity while publishing authors worldwide and appearing in English. Its archive includes a long Cambridge-published period visible in older digital collections, when Cambridge University Press distributed the ESAIM journals, before the titles consolidated under EDP Sciences; researchers tracing older volumes may therefore encounter the journal on both platforms, under the earlier ISSN pair. That is a holdings question, not an identity question: the journal, its abbreviation and its editorial line are continuous.

Open Access Through Subscribe to Open

M2AN is one of the journals in the EDP Sciences–SMAI Subscribe to Open programme, described by its publishers as a path that made its mathematics journals, in their words, the first mathematics journals in the world to transition to open access using Subscribe to Open. Under that model, libraries' subscription support opens the year's content rather than authors paying a per-article charge to make their own paper open; the publishers issue annual transparency reports on the programme, including a 2024 report covering the ESAIM and RAIRO mathematics titles. Authors should confirm the current year's arrangement on the journal's own site, esaim-m2an.org, before submitting, because Subscribe to Open operates year by year and the status of a given volume depends on that year's support. For readers, the practical consequence is simple: recent M2AN content is openly readable through the journal site, which has materially widened the audience for a journal whose papers were once reached mainly through institutional subscriptions.

Indexing, Metrics and Standing

The journal's formal standing is anchored in the Web of Science: Science Citation Index Expanded coverage, as recorded by Clarivate, with the publisher address in Les Ulis and the current ISSN pair. The older record on this site carries an h-index of 88, a figure consistent with a journal that has published influential numerical analysis for decades; h-index and quartile figures vary by source and year, and anyone citing a specific metric for evaluation should take it from the current edition of Scopus, SCImago or Journal Citation Reports rather than from this profile. What does not vary is the journal's reputation within its community: M2AN is one of the established European venues for the mathematical analysis of numerical methods, read by the researchers who design finite element, finite volume, spectral and splitting methods and who need proofs, not only results. Its papers are cited in method development across computational science, and its archive — extending, on the older site record, across coverage from 1996 to the present for the ESAIM period, with predecessor titles reaching further back — forms part of the canonical literature of numerical analysis.

How to Publish in M2AN: A Practical Guide

Begin with fit. State, in the introduction, what is modelled or discretised, what is proved, and what is computed; if any leg of that tripod is missing, the manuscript is probably for another journal. Write the analysis to the journal's standard: precise function spaces and assumptions, theorems with proofs or clear proof strategies, error estimates stated with their dependence on mesh and parameters, and stability addressed rather than assumed. Make the computations earn their place: they should verify convergence orders, expose the behaviour the theory predicts, and explore at least one case the theory does not fully cover, so the numerics add knowledge. Situate the work in the journal's own literature — M2AN readers expect engagement with prior analysis in its pages and in the neighbouring ESAIM and RAIRO titles. Follow the journal's submission instructions on esaim-m2an.org for format and process, and check the current Subscribe to Open status there. Finally, be patient with review in a journal of this type: rigorous analysis is refereed by specialists who check proofs, and revision cycles that strengthen estimates or add a decisive numerical test are a normal part of publishing here.

Reading and Using the Journal

For researchers outside pure numerical analysis — engineers, physicists, computational scientists — M2AN is most useful as a reliability filter. When a method matters to a project, its M2AN literature tells you whether convergence is proved or merely observed, in which norms, under which assumptions on data and geometry, and where the method is known to struggle. For mathematicians, it is a primary venue and a primary source. For librarians and evaluators, the identifier history is the main trap: catalogue and assessment records must connect 0764-583X and 1290-3841 with 2822-7840 and 2804-7214 as one continuing journal, or citation counts and holdings will split artificially — the same trap that produced two records for this journal on this very site.

Frequently Asked Questions

What does M2AN stand for? Mathematical Modelling and Numerical Analysis — the journal's full title is ESAIM: Mathematical Modelling and Numerical Analysis.

Who publishes it? EDP Sciences, of Les Ulis, France, within the ESAIM series associated with SMAI, the French applied and industrial mathematics society.

What are its ISSNs? Currently 2822-7840 and eISSN 2804-7214, per Clarivate's Master Journal List; earlier records carry 0764-583X and 1290-3841.

Is it indexed in Web of Science? Yes — Science Citation Index Expanded, with Current Contents Physical, Chemical and Earth Sciences and Essential Science Indicators also listed by Clarivate.

Is it open access? It participates in the EDP Sciences–SMAI Subscribe to Open programme; check the journal site for the current year's status, since the model operates annually.

Note on duplicate records: This journal also appears on this site as post 10051, “ESAIM: Mathematical Modelling and Numerical Analysis”, carrying ISSNs 2804-7214 and 2822-7840, an h-index of 88 and a thin profile. The two records share the current ISSN pair and the same title and publisher, EDP Sciences; they represent one journal. No merge has been performed in preparing this profile, and the pair is flagged for the site's standing duplicate process.

Topics and Methods in the Journal's Pages

A closer look at the methods M2AN favours helps authors judge fit before they write. Finite element analysis is a historic strength, in the French tradition of variational methods: formulation in Sobolev spaces, a priori error estimates, a posteriori estimation and adaptivity. Finite volume and discontinuous Galerkin methods for conservation laws appear with the same expectation of proof — stability, entropy or energy arguments, convergence to weak solutions where that is the right standard. Spectral and high-order methods appear where the application rewards them, as in the Fokker–Planck work described earlier, where a Maxwellian-weighted spectral Galerkin method matched the structure of a degenerate kinetic problem. Splitting and exponential integrators for evolutionary equations, including Schrödinger-type problems from electron dynamics, appear with careful error analysis rather than numerical demonstration alone. Homogenisation, asymptotic analysis and singular perturbation connect modelling to analysis when scales separate. Optimisation and inverse problems enter when they are tied to partial differential equations and computation. In every case the pattern repeats: a model with a real computational use, a discretisation or algorithm, a theorem that disciplines expectations, and experiments that test the theorem. Papers that supply all four are the journal's centre of gravity; papers that supply three are its frontier; papers that supply two belong, in most cases, to a neighbouring ESAIM title or to an applications journal.

The application pull is equally specific. Computational fluid dynamics supplies incompressible and compressible flow problems, including the Euler questions about series solutions and blow-up that the journal has hosted across decades. Kinetic theory supplies Fokker–Planck and related equations from polymers, plasmas and rarefied gases. Continuum mechanics supplies elasticity, fracture and phase-field models. Quantum and electron dynamics supply Schrödinger equations where splitting methods must respect structure over long times. Electromagnetism, acoustics and wave propagation supply problems where high order and dispersion control matter. Biology and medicine enter through models that are genuinely computed and analysed — population, pattern and transport models — rather than through data description. An author whose application is not on any such list should ask whether the mathematical contribution is strong enough to carry the paper on its own; an author whose mathematics is strong but whose computation is a single illustrative plot should strengthen the experiments before submitting, because the journal's own description promises its readers evidence of computational relevance, and referees enforce the promise.

Editorial Expectations and the Life of a Paper

Refereeing in a journal of this kind is expert and exacting. Referees check proofs, probe assumptions — a regularity hypothesis that excludes the paper's own numerical example will be noticed — and ask whether experiments measure what the theorems predict. Authors should therefore write for that reader: number the assumptions, state theorems before the computations that illustrate them, report observed convergence orders in tables beside the predicted orders, and discuss discrepancies instead of smoothing them over. Notation discipline matters; so does honesty about parameter regimes, mesh limits and the cost of the method. The reward for meeting the standard is durability. A proved method in M2AN enters the reference literature of its problem class and is still being cited when purely numerical demonstrations of the same vintage have been superseded, which is one reason the journal's h-index, carried as 88 on its older record here, accumulated at all. The journal's Subscribe to Open status adds a second reward: work published in an open year is readable by every potential user, including the engineers and scientists whose adoption ultimately validates a numerical method.

For the wider system, M2AN performs a certification function. Funding panels, hiring committees and software projects all need to know which methods are understood and which are merely promising; a method with an M2AN analysis behind it carries that certification in a compact, checkable form. That function depends on the journal refusing to lower its double test — rigorous theoretical analysis and evidence of computational relevance — and its publisher states the test in a single sentence precisely so that authors, referees and readers can all hold the journal to it. Profiles of the journal, including this one, should do the same: describe M2AN neither as a general applied-mathematics outlet nor as a pure-analysis journal, but as the specific, demanding meeting point of modelling, proof and computation that its name announces.

A final note on records will save researchers real time. When searching for this journal, use the abbreviation M2AN alongside the full title, and connect all four ISSNs in a single search strategy: the earlier pair 0764-583X and 1290-3841 retrieves the journal's earlier EDP Sciences and Cambridge-distributed literature, while the current pair 2822-7840 and 2804-7214 retrieves its present Web of Science record and Subscribe to Open volumes. Citation databases that treat the pairs as separate journals will understate the journal's influence and split an author's publication record; authors preparing evaluation dossiers should therefore list the ISSN relevant to each paper's year and note the continuity explicitly. The same advice applies to the duplicate records on this site, flagged in this profile: two thin records became two partial pictures of one substantial journal, and restoring a single, complete picture — in catalogues, in dossiers and in directories like this one — is a small but genuine service to the researchers who rely on those records to choose where to read and where to publish.

Editors preparing this profile checked every factual claim against the publisher's and the journal's own published descriptions and against the records held on this site, and left any operational detail that could not be verified in that way — current charges, timelines or board lists that change without notice — for readers to confirm on the journal's official home at the moment they need it. That restraint is deliberate: a directory profile should be a reliable starting point for further enquiry, not a source of confidently repeated figures that were already out of date when they were copied.