• 452 Citations
  • 13 h-Index
19962020

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Article
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 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., Oct 1 2018, In : Journal of Computational and Applied Mathematics. 340, p. 424-431 8 p.

Research output: Contribution to journalArticle

2016
1 Citation (Scopus)
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

4 Citations (Scopus)

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

21 Citations (Scopus)
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)
12 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)
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)
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

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

18 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

35 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

19 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

66 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)

Sobolev regularity of the second biharmonic problem on a rectangle

Karátson, J., Oct 1 2005, In : Acta Mathematica Hungarica. 109, 3, p. 255-259 5 p.

Research output: Contribution to journalArticle

2004

Conditioning analysis of separate displacement preconditioners for some nonlinear elasticity systems

Axelsson, O. & Karátson, J., Mar 10 2004, In : Mathematics and Computers in Simulation. 64, 6, p. 649-668 20 p.

Research output: Contribution to journalArticle

6 Citations (Scopus)

Constructive Sobolev gradient preconditioning for semilinear elliptic systems

Karátson, J., May 21 2004, In : Electronic Journal of Differential Equations. 2004, p. 1-26 26 p.

Research output: Contribution to journalArticle

11 Citations (Scopus)

Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators

Axelsson, O. & Karátson, J., Dec 1 2004, In : Numerische Mathematik. 99, 2, p. 197-223 27 p.

Research output: Contribution to journalArticle

22 Citations (Scopus)
2003
10 Citations (Scopus)

Symmetric part preconditioning for the conjugate gradient method in Hilbert space

Axelsson, O. & Karátson, J., Jan 1 2003, In : Numerical Functional Analysis and Optimization. 24, 5-6, p. 455-474 20 p.

Research output: Contribution to journalArticle

13 Citations (Scopus)

Variable preconditioning via quasi-Newton methods for nonlinear problems in Hilbert space

Karátson, J. & Faragó, I., Aug 1 2003, In : SIAM Journal on Numerical Analysis. 41, 4, p. 1242-1262 21 p.

Research output: Contribution to journalArticle

21 Citations (Scopus)
2002

A concept of energy Banach space and its application to the gradient method

Karátson, J., Mar 15 2002, In : Journal of Mathematical Analysis and Applications. 267, 2, p. 548-563 16 p.

Research output: Contribution to journalArticle

On the rate of convergence of the conjugate gradient method for linear operators in Hilbert space

Axelsson, O. & Karátson, J., May 2002, In : Numerical Functional Analysis and Optimization. 23, 3-4, p. 285-302 18 p.

Research output: Contribution to journalArticle

12 Citations (Scopus)

Sobolev space preconditioning for Newton's method using domain decomposition

Axelsson, O., Faragó, I. & Karátson, J., Jan 1 2002, In : Numerical Linear Algebra with Applications. 9, 6-7, p. 585-598 14 p.

Research output: Contribution to journalArticle

10 Citations (Scopus)
2001

Gradient-finite element method for nonlinear neumann problems

Faragó, I. & Karátson, J., Dec 2001, In : Journal of Applied Analysis. 7, 2, p. 257-269 13 p.

Research output: Contribution to journalArticle

On the gradient method for some nonlinear elliptic boundary value problems

Karátson, J., Dec 1 2001, In : Acta Mathematica Hungarica. 93, 1-2, p. 115-133 19 p.

Research output: Contribution to journalArticle