M. Rokyta

 

List of selected publications in English

Google Scholar profile

Monographs

  • Málek J., Nečas J., Rokyta M., Růžička M.: Weak and measure-valued solutions to evolutionary partial differential equations. Chapman & Hall, 1996.

Scientific articles in journals or conference proceedings

  • Feistauer M., Kalis H., Rokyta M.: Mathematical modelling of an electrolysis process. Comment. Math. Univ. Carolin. 30 (1989), no. 3, 465-477. [MR 91d:35081]

  • Feistauer M., Felcman J., Rokyta M., Vlášek Z.: Finite element solution of flow problems with trailing conditions J. Comput. Appl. Math. 44 (1992), no.2, 131-165. [MR 94d:76052]

  • Kröner D., Rokyta M.: Convergence of upwind finite volume schemes for scalar conservation laws in 2D. SIAM J. Numer. Anal. 31 (1994), no. 2, 324-343. [Zbl 930.53894], [MR 95e:65085]

  • Kröner D., Noelle S., Rokyta M.: Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions. Numer. Math. 71 (1995), no. 4, 527-560. [Zbl 841.65079], [MR 96j:65087]

  • Kröner D., Rokyta M., Wierse M.: Finite volume methods of higher order for conservation laws and convection dominated diffusion equations. In: Proceedings of the 2nd Seminar Euler and Navier-Stokes Equations, Kozel K., Příhoda J. (eds.), pp. 41-44, Institute of Thermomechanics AS CR Prague, 1996. [ISBN: 80-85918-18-8]

  • Kröner D., Rokyta M., Wierse, M.: A Lax-Wendroff type theorem for upwind finite volume schemes in 2D. East-West J. Numer. Math. 4 (1996), no. 4, 279-292.

  • Kröner D., Rokyta M.: Higher order finite volume method for convection dominated diffusion equation in 2D. In: Numerical Modelling in Continuum Mechanics, Feistauer M., Rannacher R., Kozel K. (eds.), pp. 62-70, Matfyzpress, Praha 1997. [ISBN: 80-85863-25-1]

  • Rokyta M.: On the solvability of a nonlinear discrete problem corresponding to a higher-order finite volume approximation in 2D. East-West J. of Num. Math. 7, no.3 (1999), 187-197.

  • Rokyta, M.: Replacing h by h2. In: Applied Nonlinear Analysis, Sequeira, A. et al. (eds.), pp. 469-484, Kluwer Academic / Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 1999.

  • Feistauer M., Dolejsi V., Felcman J., Klikova A., Rokyta M.: Numerical schemes for nonlinear convection-diffusion problems. In: Proceedings of the XIIIth Summer School Software and Algorithms of Numerical Mathematics, 51-74 , ed. University of West Bohemia, Plzeň, 1999, [ISBN 80-7082-566-9].

  • Rokyta M.: A suitable replacement of the BV condition for finite volume schemes on unstructured grids. In: Numerical Modelling in Continuum Mechanics, Feistauer M., Rannacher R., Kozel K. (eds.), pp. 267-274, Matfyzpress, Praha, 2001. [ISBN: 80-85863-67-7]

  • Černý R., Kolář J., Rokyta M.: Monotone measures with bad tangential behavior in the plane. Comment. Math. Univ. Carolin. 52,3 (2011), 317-339.

  • Černý R., Kolář J., Rokyta M.: Concentrated monotone measures with non-unique tangential behavior in $R^3$. Czech. Math. Jour. 61 (136) (2011), 1141-1167.

  • Kröner D., Rokyta M. A priori error estimates for upwind finite volume schemes for two-dimensional linear convection diffusion problems. Bull. Braz. Math. Soc, New series. 47(2) (2016), 473-488.

  • Kröner D., Rokyta M. Error estimates for higher-order finite volume schemes for convection diffusion problems. Journal of Numerical Mathematics., vol. 26 (1), (2018), 35-62. DOI: https://doi.org/10.1515/jnma-2016-1056.

  • Kröner D., Mackeben Th., Rokyta M.: Nonconvergence proof for the LDA-scheme. In: Proceedings of the XVII International Conference(HYP2018) on “Hyperbolic Problems: Theory, Numerics, Applications”, by Alberto Bressan, Marta Lewicka, Dehua Wang, Yuxi Zheng (Eds.), AIMS on Applied Mathematics, Vol. 10, pp. 507-514, 2020. ISBN-10: 1-60133-023-5, ISBN-13: 978-1-60133-023-9.

Textbooks in English

  • Černý I., Rokyta M.: Differential and integral calculus of one real variable. Textbook for students of MFF UK (in English). Karolinum, 1998. [ISBN 80-7184-661-9]

Editorial work

  • Málek J., Nečas J., Rokyta M. (eds.): Advanced topics in theoretical fluid mechanics, Pitman Research Notes in Mathematics Series 392, (the Proceedings of the Fifth Winter School, Paseky, December 1997), Addison Wesley Longman, 1998.

  • Málek J., Nečas J., Rokyta M. (eds.): Advances in Mathematical Fluid Mechanics Lecture notes of the sixth international school "Mathematical theory in fluid mechanics", Paseky, Czech Republic, Sept. 19-25, 1999, Springer Verlag, Berlin-Heidelberg-New York, 2000. [ISBN 3-540-67786-0]

  • E. Feireisl, J. Málek, M. Rokyta (eds.): Proceedings of the Tenth Paseky School on Mathematical Theory in Fluid Mechanics, Paseky, May 2007. Discrete and Continuous Dynamical Systems - Series S, Vol. 1, No. 3, September 2008.

  • E. Feireisl, J. Málek, M. Rokyta (eds.): Proceedings of the Eleventh School on Mathematical Theory in Fluid Mechanics, Kacov, May 2009. Discrete and Continuous Dynamical Systems - Series S, Vol. 3, No. 3, September 2010.

  • E. Feireisl, J. Málek, M. Rokyta (eds.): Proceedings of the 12th School on Mathematical Theory in Fluid Mechanics, Kacov, May-June 2011. Discrete and Continuous Dynamical Systems - Series S, Vol. 5, No. 6, December 2012.

Theses

  • Rokyta, M.: Numerical solution of strongly nonlinear elliptic problems, (in Czech). Diploma thesis, MFF UK, Praha, 1985.

  • Rokyta, M.: Euler equations and their numerical solution by the finite volume method, (in English). Ph.D. thesis, MFF UK, Praha, 1992.

  • Rokyta, M.: Theoretical analysis of the finite volume method, (Introduction in Czech). Habilitation thesis, MFF UK, Praha, 1999.