Most cited papers in Advanced Numerical Methods in Computational Mathematics
What are the most cited papers in Advanced Numerical Methods in Computational Mathematics?
The most cited paper in Advanced Numerical Methods in Computational Mathematics is "Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces" (Rainer Storn, Kenneth V. Price, 1997), with 29,587 citations. Next come "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement" (6,340) and "Element‐free Galerkin methods" (5,653).
Showing 50 of 99 papers. Every paper with more than 1,195 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces Rainer Storn, Kenneth V. Price · Journal of Global Optimization | Dec 1997 | 29,587 |
| 2 | Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Thomas J.R. Hughes, J. Austin Cottrell, Yuri Bazilevs · Computer Methods in Applied Mechanics and Engineering | Feb 2005 | 6,340 |
| 3 | Element‐free Galerkin methods Ted Belytschko, Ye Lu, Linxia Gu · International Journal for Numerical Methods in Engineering | 30 Jan 1994 | 5,653 |
| 4 | Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations A. Brooks, Thomas J.R. Hughes · Computer Methods in Applied Mechanics and Engineering | Sep 1982 | 5,374 |
| 5 | Solution of the implicitly discretised fluid flow equations by operator-splitting Raad I. Issa · Journal of Computational Physics | 1986 | 5,314 |
| 6 | High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method Urmila Ghia, K. N. Ghia, C. T. Shin · Journal of Computational Physics | Dec 1982 | 4,319 |
| 7 | Navier Stokes Equations: Theory and Numerical Analysis Roger Témam, ALEXANDRE JOEL CHORIN · Journal of Applied Mechanics | Jun 1978 | 4,051 |
| 8 | A proposed modification of the Germano subgrid-scale closure method Douglas K. Lilly · Physics of Fluids A Fluid Dynamics | Mar 1992 | 4,044 |
| 9 | The MATLAB ODE Suite Lawrence F. Shampine, Mark W. Reichelt · SIAM Journal on Scientific Computing | 1997 | 3,654 |
| 10 | The partition of unity finite element method: Basic theory and applications Jens Markus Melenk, Ivo M. Babuska · Computer Methods in Applied Mechanics and Engineering | Dec 1996 | 3,457 |
| 11 | ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS J. P. Van Doormaal, George D. Raithby · Numerical Heat Transfer | Apr 1984 | 3,450 |
| 12 | New development in freefem++ Frédéric Hecht · Journal of Numerical Mathematics | 2012 | 3,447 |
| 13 | Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn et al. · SIAM Journal on Numerical Analysis | 2002 | 3,312 |
| 14 | Mixed finite elements in ?3 Jean-Claude Nédélec · Numerische Mathematik | Sep 1980 | 3,304 |
| 15 | A fast marching level set method for monotonically advancing fronts. James A. Sethian · Proceedings of the National Academy of Sciences | 20 Feb 1996 | 3,254 |
| 16 | Meshless methods: An overview and recent developments Ted Belytschko, Y. Krongauz, D. Organ et al. · Computer Methods in Applied Mechanics and Engineering | Dec 1996 | 3,147 |
| 17 | Numerical analysis of blood flow in the heart Charles S. Peskin · Journal of Computational Physics | Nov 1977 | 3,088 |
| 18 | Application of a fractional-step method to incompressible Navier-Stokes equations John Kim, Parviz Moin · Journal of Computational Physics | Jun 1985 | 3,085 |
| 19 | Introduction to the Finite Element Method Sung W. Lee, Peter W. Chung · Cambridge University Press eBooks | 17 Jun 2021 | 2,945 |
| 20 | Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations Christian Miehé, Fabian Welschinger, Martina Hofacker · International Journal for Numerical Methods in Engineering | 22 Mar 2010 | 2,938 |
| 21 | Occam's inversion; a practical algorithm for generating smooth models from electromagnetic sounding data Steven Constable, Robert L. Parker, Catherine G. Constable · Geophysics | Mar 1987 | 2,797 |
| 22 | Local adaptive mesh refinement for shock hydrodynamics Marsha Berger, Phillip Colella · Journal of Computational Physics | May 1989 | 2,654 |
| 23 | A dual algorithm for the solution of nonlinear variational problems via finite element approximation Daniel Gabay, Bertrand Mercier · Computers & Mathematics with Applications | 1976 | 2,636 |
| 24 | SUNDIALS A.C. Hindmarsh, Peter N. Brown, Keith Eric Grant et al. · ACM Transactions on Mathematical Software | Sep 2005 | 2,634 |
| 25 | Total variation diminishing Runge-Kutta schemes Sigal Gottlieb, Chi‐Wang Shu · Mathematics of Computation | 1998 | 2,563 |
| 26 | Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection Bram van Leer · Journal of Computational Physics | Mar 1977 | 2,468 |
| 27 | A Numerical Method for Solving Incompressible Viscous Flow Problems ALEXANDRE JOEL CHORIN · Journal of Computational Physics | Aug 1997 | 2,460 |
| 28 | The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems Bernardo Cockburn, Chi‐Wang Shu · SIAM Journal on Numerical Analysis | 1998 | 2,432 |
| 29 | Mixed and Hybrid Finite Element Methods Franco Brezzi, Michel Fortin · CERN Document Server (European Organization for Nuclear Research) | 23 Nov 2011 | 2,420 |
| 30 | A simple error estimator and adaptive procedure for practical engineerng analysis Olgierd Cecil Zienkiewicz, J.Z. Zhu · International Journal for Numerical Methods in Engineering | Feb 1987 | 2,410 |
| 31 | An arbitrary Lagrangian-Eulerian computing method for all flow speeds C.W. Hirt, A.A. Amsden, J.L. Cook · Journal of Computational Physics | Mar 1974 | 2,404 |
| 32 | THE PARTITION OF UNITY METHOD Ivo M. Babuska, Jens Markus Melenk · International Journal for Numerical Methods in Engineering | 28 Feb 1997 | 2,368 |
| 33 | A spectral element method for fluid dynamics: Laminar flow in a channel expansion Anthony T. Patera · Journal of Computational Physics | Jun 1984 | 2,347 |
| 34 | Numerical solution of saddle point problems Michele Benzi, Gene Howard Golub, Jörg Liesen · Acta Numerica | 19 Apr 2005 | 2,339 |
| 35 | A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics Satya N. Atluri, Tengteng Zhu · Computational Mechanics | 24 Aug 1998 | 2,337 |
| 36 | Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes A. Jameson, Wolfgang M. Schmidt, Eli Turkel | 23 Jun 1981 | 2,334 |
| 37 | Level Set Methods: An Overview and Some Recent Results Stanley Osher, Ronald P. Fedkiw · Journal of Computational Physics | May 2001 | 2,308 |
| 38 | Homogenization and Two-Scale Convergence Grégoire Allaire · SIAM Journal on Mathematical Analysis | Nov 1992 | 2,295 |
| 39 | A mixed finite element method for 2-nd order elliptic problems Pierre-Arnaud Raviart, J. M. Thomas · Lecture notes in mathematics | 1977 | 2,224 |
| 40 | A posteriori error estimation in finite element analysis Mark Andrew Ainsworth, J. Tinsley Oden · Computer Methods in Applied Mechanics and Engineering | Mar 1997 | 2,193 |
| 41 | A Method for the Numerical Calculation of Hydrodynamic Shocks J. VonNeumann, Robert D. Richtmyer · Journal of Applied Physics | Mar 1950 | 2,192 |
| 42 | Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model Akio Arakawa, V. R. Lamb · Methods in computational physics | 1977 | 2,158 |
| 43 | Distance Regularized Level Set Evolution and Its Application to Image Segmentation Chunming Li, Chenyang Xu, Changfeng Gui et al. · IEEE Transactions on Image Processing | 27 Aug 2010 | 2,126 |
| 44 | Adaptive mesh refinement for hyperbolic partial differential equations Marsha Berger, Joseph Oliger · Journal of Computational Physics | Mar 1984 | 2,067 |
| 45 | Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations Edward J. Kansa · Computers & Mathematics with Applications | 1990 | 2,064 |
| 46 | The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique Olgierd Cecil Zienkiewicz, J.Z. Zhu · International Journal for Numerical Methods in Engineering | 30 May 1992 | 2,020 |
| 47 | The FEniCS Project Version 1.5 Martin Sandve Alnæs, Jan Blechta, Johan E. Hake et al. · Department of Earth Sciences EPrints Repository | 2015 | 1,987 |
| 48 | Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates Edward J. Kansa · Computers & Mathematics with Applications | 1990 | 1,965 |
| 49 | TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework Bernardo Cockburn, Chi‐Wang Shu · Mathematics of Computation | 1989 | 1,945 |
| 50 | Mesh Free Methods: Moving Beyond the Finite Element Method GR Liu, Dimitrios Karamanlidis · Applied Mechanics Reviews | Mar 2003 | 1,933 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.