Most-cited papers on numerical verify problems coercivity sufficient

Ranked by citation count via OpenAlex. Citations update on a rolling basis; list regenerates every 24h.

1. Verification of numerical procedures for the analysis of soil liquefaction problems

   1993 · Arulanandan, Kandiah, Scott, Ronald F.

   213 cited

2. A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem

   1998 · SIAM Journal on Numerical Analysis · Yamamoto, Nobito

   119 cited

3. On the Inverse Problem of Rectangular Plates Subjected to Elastic Impact, Part I: Method Development and Numerical Verification

   1995 · Journal of Applied Mechanics · Yen, Ching-Shih, Wu, Enboa

   84 cited

4. A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems

   2005 · Computing · Nakao, Mitsuhiro T., Hashimoto, Kouji, Watanabe, Yoshitaka

   74 cited

5. C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems

   1997 · Springer eBooks · Hammer, Rolf, Ratz, D., Kulisch, Ulrich et al.

   72 cited

6. A numerical verification method for the existence of weak solutions for nonlinear boundary value problems

   1992 · Journal of Mathematical Analysis and Applications · Nakao, Mitsuhiro T.

   71 cited

7. C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Programs

   1995 · Hammer, Rolf, Hocks, Matthias, Kulisch, Ulrich et al.

   41 cited

8. Numerical and experimental verification of two methods for solving an inverse heat conduction problem

   2015 · International Journal of Heat and Mass Transfer · Duda, P.

   39 cited

9. An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness

   1999 · Numerical Functional Analysis and Optimization · Nagatou, Kaori, Yamamoto, Norifumi, Nakao, Mitsuhiro T.

   36 cited

10. Numerical Verification of Solutions for Nonlinear Elliptic Problems Using anL∞Residual Method

    1998 · Journal of Mathematical Analysis and Applications · Nakao, Mitsuhiro T., Yamamoto, Nobito

    36 cited

11. Numerical Toolbox for Verified Computing I : Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs

    2011 · Hammer, Rolf, Hocks, Matthias, Kulisch, Ulrich et al.

    34 cited

12. A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem

    2004 · Journal of Mathematical Fluid Mechanics · Watanabe, Yoshitaka, Yamamoto, Nobito, Nakao, Mitsuhiro T. et al.

    31 cited

13. Numerical verification methods for solutions of semilinear elliptic boundary value problems

    2011 · Nonlinear Theory and Its Applications IEICE · Nakao, Mitsuhiro T., Watanabe, Yoshitaka

    30 cited

14. Numerical and experimental verification of the single neural adaptive PID real-time inverse method for solving inverse heat conduction problems

    2022 · International Journal of Heat and Mass Transfer · Wan, Shibin, Wang, Kun, Xu, Peng et al.

    28 cited

15. A numerical stress based approach for predicting failure in NBG-18 nuclear graphite components with verification problems

    2012 · Journal of Nuclear Materials · Hindley, Michael P., Mitchell, Mark N., Erasmus, Christiaan et al.

    26 cited

16. Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification

    2016 · Nonlinearity · Capiński, Maciej J, Gidea, Marian, Llave, Rafael de la

    23 cited

17. Verification and validation considerations regarding the qualification of numerical schemes for LES for dilution problems

    2010 · Nuclear Engineering and Design · Ducros, F., Bieder, Ulrich, Cioni, O. et al.

    22 cited

18. A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh–Bénard problems

    2008 · Numerische Mathematik · Kim, Myoungnyoun, Nakao, Mitsuhiro, Watanabe, Yoshitaka et al.

    21 cited

19. A NUMERICAL SCHEME FOR NON-FOURIER HEAT CONDUCTION, PART II: TWO-DIMENSIONAL PROBLEM FORMULATION AND VERIFICATION

    2002 · Numerical Heat Transfer Part B Fundamentals · Lam, Tung T., Yeung, Wing K.

    20 cited

20. Numerical verification of stationary solutions for Navier–Stokes problems

    2006 · Journal of Computational and Applied Mathematics · Nagatou, Kaori, Hashimoto, Kouji, Nakao, Mitsuhiro T.

    20 cited

21. Efficiency and Accuracy Verification of the Explicit Numerical Manifold Method for Dynamic Problems

    2014 · Rock Mechanics and Rock Engineering · Qu, X. L., Wang, Y., Fu, Guoyang et al.

    20 cited

22. Experimental Model Design and Preliminary Numerical Verification of Fluid–Thermal–Structural Coupling Problem

    2019 · AIAA Journal · Liu, Lei, Guangyue, Dai, Zeng, Lei et al.

    20 cited

23. Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems

    2000 · Journal of Optimization Theory and Applications · Helmes, Kurt, Stockbridge, Richard H.

    20 cited

24. Development and Verification of a Numerical Library for Solving Global Terrestrial Multiphysics Problems

    2019 · Journal of Advances in Modeling Earth Systems · Bisht, Gautam, Riley, W. J.

    19 cited

25. Numerical Toolbox for Verified Computing II: Advanced Numerical Problems

    2009 · Krämer, Walter, Kulisch, Ulrich, Löhner, Rainald

    18 cited

26. A Numerical Method to Verify the Elliptic Eigenvalue Problems Including a Uniqueness Property

    1999 · Computing · Nagatou, Kaori

    18 cited

27. Verifying the suitability of uncoupled numerical methods for solving vehicle-bridge interaction problems

    2022 · Structure and Infrastructure Engineering · González, Arturo, Regales, Enrique Covián, Casero, Miguel

    18 cited

28. Numerical verification of a non-residual orthogonal term-by-term stabilized finite element formulation for incompressible convective flow problems

    2020 · Computers & Mathematics with Applications · González, Amaru, Castillo, Ernesto, Cruchaga, M

    16 cited

29. Numerical verification of solutions for elasto-plastic torsion problems

    2000 · Computers & Mathematics with Applications · Nakao, Mitsuhiro, Lee, S.H., Ryoo, C. S.

    14 cited