• 441 Citations
  • 13 h-Index
19962020

Research output per year

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Research Output

2020
2019

Qualitative properties of discrete nonlinear parabolic operators

Horváth, R., Faragó, I. & Karátson, J., Nov 1 2019, In : Numerische Mathematik. 143, 3, p. 529-554 26 p.

Research output: Contribution to journalArticle

Open Access

Variable preconditioning for strongly nonlinear elliptic problems

Borsos, B. & Karátson, J., Apr 1 2019, In : Journal of Computational and Applied Mathematics. 350, p. 155-164 10 p.

Research output: Contribution to journalArticle

2018

Qualitative properties of nonlinear parabolic operators II: the case of PDE systems

Csóka, J., Faragó, I., Horváth, R., Karátson, J. & Korotov, S., Dec 1 2018, In : Journal of Mathematical Analysis and Applications. 468, 1, p. 64-86 23 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems

Axelsson, O. & Karátson, J., Jul 4 2018, In : Numerical Functional Analysis and Optimization. 39, 9, p. 921-936 16 p.

Research output: Contribution to journalArticle

Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations

Axelsson, O., Karátson, J. & Magoulès, F., Jan 1 2018, (Accepted/In press) In : Journal of Computational and Applied Mathematics.

Research output: Contribution to journalArticle

2016
1 Citation (Scopus)
2015

Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems

Axelsson, O., Blaheta, R., Byczanski, P., Karátson, J. & Ahmad, B., May 15 2015, In : Journal of Computational and Applied Mathematics. 280, p. 141-157 17 p.

Research output: Contribution to journalArticle

6 Citations (Scopus)

Some discrete maximum principles arising for nonlinear elliptic finite element problems

Karátson, J. & Korotov, S., Dec 2015, In : Computers and Mathematics with Applications. 70, 11, p. 2732-2741 10 p.

Research output: Contribution to journalArticle

2014

Reaching the superlinear convergence phase of the CG method

Axelsson, O. & Karátson, J., Jan 1 2014, In : Journal of Computational and Applied Mathematics. 260, p. 244-257 14 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

Robust preconditioning estimates for convection-dominated elliptic problems via a streamline Poincaré-Friedrichs inequality

Axelsson, O., Karátson, J. & Kovács, B., Jan 1 2014, In : SIAM Journal on Numerical Analysis. 52, 6, p. 2957-2976 20 p.

Research output: Contribution to journalArticle

2013

A Preconditioned Iterative Solution Scheme for Nonlinear Parabolic Systems Arising in Air Pollution Modeling

Karátson, J. & Kurics, T., Dec 30 2013, In : Mathematical Modelling and Analysis. 18, 5, p. 641-653 13 p.

Research output: Contribution to journalArticle

3 Citations (Scopus)

Editors' preface for the topical issue "Numerical Methods for Large-Scale Scientific Computing, I"

Karátson, J., Korotov, S. & Margenov, S., Feb 6 2013, In : Central European Journal of Mathematics. 11, 4, p. 595-596 2 p.

Research output: Contribution to journalEditorial

Editors' preface for the topical issue "Numerical Methods for Large-Scale Scientific Computing, II"

Karátson, J., Korotov, S. & Margenov, S., Aug 1 2013, In : Central European Journal of Mathematics. 11, 8, p. 1359-1360 2 p.

Research output: Contribution to journalEditorial

Harmonic averages, exact difference schemes and local Green's functions in variable coefficient PDE problems

Axelsson, O. & Karátson, J., Aug 1 2013, In : Central European Journal of Mathematics. 11, 8, p. 1441-1457 17 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)
2012
2 Citations (Scopus)

Discrete maximum principles for nonlinear parabolic PDE systems

Faragó, I., Karátson, J. & Korotov, S., Oct 1 2012, In : IMA Journal of Numerical Analysis. 32, 4, p. 1541-1573 33 p.

Research output: Contribution to journalArticle

20 Citations (Scopus)

Operator preconditioning with efficient applications for nonlinear elliptic problems

Karátson, J., Feb 1 2012, In : Central European Journal of Mathematics. 10, 1, p. 231-249 19 p.

Research output: Contribution to journalReview article

2011

Discrete maximum principles for FEM solutions of nonlinear elliptic systems

Karátson, J. & Korotov, S., Dec 1 2011, Computational Mathematics: Theory, Methods and Applications. Nova Science Publishers, Inc., p. 213-260 48 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Preface

Axelsson, O. & Karátson, J., Dec 1 2011, Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations. Bentham Science Publishers Ltd., p. iii

Research output: Chapter in Book/Report/Conference proceedingForeword/postscript

Open Access
2010

A discrete maximum principle for nonlinear elliptic systems with interface conditions

Karátson, J., Jun 25 2010, Large-Scale Scientific Computing - 7th International Conference, LSSC 2009, Revised Papers. p. 580-587 8 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 5910 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Numerical Preconditioning Methods for Elliptic PDEs

Karátson, J., Jan 1 2010, Sobolev Gradients and Differential Equations. Springer Verlag, p. 245-257 13 p. (Lecture Notes in Mathematics; vol. 1670).

Research output: Chapter in Book/Report/Conference proceedingChapter

2009

Condition number analysis for various forms of block matrix preconditioners

Axelsson, O. & Karátson, J., Dec 1 2009, In : Electronic Transactions on Numerical Analysis. 36, p. 168-194 27 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)
11 Citations (Scopus)

Discrete maximum principles for the FEM solution of some nonlinear parabolic problems

István, F., Karátson, J. & Sergey, K., Dec 1 2009, In : Electronic Transactions on Numerical Analysis. 36, p. 149-167 19 p.

Research output: Contribution to journalArticle

8 Citations (Scopus)

Equivalent operator preconditioning for elliptic problems

Axelsson, O. & Karátson, J., Mar 1 2009, In : Numerical Algorithms. 50, 3, p. 297-380 84 p.

Research output: Contribution to journalArticle

15 Citations (Scopus)
5 Citations (Scopus)

On superlinear PCG methods for FDM discretizations of convection-Diffusion equations

Karátson, J. & Kurics, T., Jul 20 2009, Numerical Analysis and Its Applications - 4th International Conference, NAA 2008, Revised Selected Papers. p. 345-352 8 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 5434 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Some superlinear PCG methods for discretized elliptic problems

Karátson, J. & Kurics, T., Dec 1 2009, Computational Methods in Science and Engineering - Advances in Computational Science, Lectures Presented at the Int. Conference on Computational Methods in Science and Engineering 2008, ICCMSE 2008. p. 861-864 4 p. (AIP Conference Proceedings; vol. 1148 2).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2008

A mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems

Antal, I. & Karátson, J., May 1 2008, In : Computers and Mathematics with Applications. 55, 10, p. 2185-2196 12 p.

Research output: Contribution to journalArticle

7 Citations (Scopus)

Mesh independent convergence rates via differential operator pairs

Axelsson, O. & Karátson, J., Dec 1 2008, Large-Scale Scientific Computing - 6th International Conference, LSSC 2007, Revised Papers. p. 3-15 13 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 4818 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems

Karátson, J. & Kurics, T., Mar 1 2008, In : Journal of Computational and Applied Mathematics. 212, 2, p. 214-230 17 p.

Research output: Contribution to journalArticle

8 Citations (Scopus)

Superlinear PCG algorithms: Symmetric part preconditioning and boundary conditions

Karátson, J., May 1 2008, In : Numerical Functional Analysis and Optimization. 29, 5-6, p. 590-611 22 p.

Research output: Contribution to journalArticle

3 Citations (Scopus)
2007

A parallel algorithm for systems of convection-diffusion equations

Karátson, J., Kurics, T. & Lirkov, I., Oct 29 2007, Numerical Methods and Applications - 6th International Conference, NMA 2006, Revised Papers. p. 65-73 9 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 4310 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Double Sobolev gradient preconditioning for nonlinear elliptic problems

Axelsson, O. & Karátson, J., Sep 1 2007, In : Numerical Methods for Partial Differential Equations. 23, 5, p. 1018-1036 19 p.

Research output: Contribution to journalArticle

Mesh independent superlinear PCG rates via compact-equivalent operators

Axelssont, O. W. E. & Karátson, J., Dec 1 2007, In : SIAM Journal on Numerical Analysis. 45, 4, p. 1495-1516 22 p.

Research output: Contribution to journalArticle

17 Citations (Scopus)

Newton's method in the context of gradients

Karátson, J. & Neuberger, J. W., Sep 24 2007, In : Electronic Journal of Differential Equations. 2007, p. 1-13 13 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)

On discrete maximum principles for nonlinear elliptic problems

Karátson, J., Korotov, S. & Křížek, M., Oct 12 2007, In : Mathematics and Computers in Simulation. 76, 1-3, p. 99-108 10 p.

Research output: Contribution to journalArticle

34 Citations (Scopus)
2 Citations (Scopus)

Symmetric part preconditioning of the CG method for stokes type saddle-point systems

Axelsson, O. & Karátson, J., Sep 1 2007, In : Numerical Functional Analysis and Optimization. 28, 9-10, p. 1027-1049 23 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)
2006
9 Citations (Scopus)

Multiplicity for semilinear elliptic equations involving singular nonlinearity

Hernández, J., Karátson, J. & Simon, P. L., Jul 15 2006, In : Nonlinear Analysis, Theory, Methods and Applications. 65, 2, p. 265-283 19 p.

Research output: Contribution to journalArticle

18 Citations (Scopus)
2005

Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions

Karátson, J. & Korotov, S., Feb 1 2005, In : Numerische Mathematik. 99, 4, p. 669-698 30 p.

Research output: Contribution to journalArticle

64 Citations (Scopus)
5 Citations (Scopus)

Preconditioning operators and Sobolev gradients for nonlinear elliptic problems

Karátson, J. & Faragó, I., Oct 1 2005, In : Computers and Mathematics with Applications. 50, 7, p. 1077-1092 16 p.

Research output: Contribution to journalArticle

19 Citations (Scopus)

Sobolev gradient preconditioning for the electrostatic potential equation

Karátson, J. & Lóczi, L., Oct 1 2005, In : Computers and Mathematics with Applications. 50, 7, p. 1093-1104 12 p.

Research output: Contribution to journalArticle

13 Citations (Scopus)