Petr Knobloch

Research interests

Publications

Curriculum vitae

Teaching


 List of publications

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  1. Knobloch, P., Kuzmin, D., Jha, A.: Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations, submitted download

  2. Heydari, Sh., Knobloch, P., Wick, T.: Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model, J. Comput. Phys. 499 (2024), Art. No. 112711, 19 pp. download

  3. Barrenechea, G.R., John, V., Knobloch, P.: Finite element methods respecting the discrete maximum principle for convection-diffusion equations, SIAM Rev. 66 (2024), 3-88 download

  4. John, V., Knobloch, P., Pártl, O.: A numerical assessment of finite element discretizations for convection-diffusion-reaction equations satisfying discrete maximum principles, Comput. Methods Appl. Math. 23 (2023), 969-988 download

  5. Knobloch, P.: An algebraically stabilized method for convection-diffusion-reaction problems with optimal experimental convergence rates on general meshes, Numer. Algorithms 94 (2023), 547-580 download

  6. Jha, A., John, V., Knobloch, P.: Adaptive grids in the context of algebraic stabilizations for convection-diffusion-reaction equations, SIAM J. Sci. Comput. 45 (2023), B564-B589 download

  7. Fuest, M., Heydari, Sh., Knobloch, P., Lankeit, J., Wick, T.: Global existence of classical solutions and numerical simulations of a cancer invasion model, ESAIM Math. Model. Numer. Anal. 57 (2023), 1893-1919 download

  8. John, V., Knobloch, P., Wilbrandt, U.: A posteriori optimization of parameters in stabilized methods for convection-diffusion problems - Part II, J. Comput. Appl. Math. 428 (2023), Art. No. 115167, 17 pp. download

  9. John, V., Knobloch, P.: On algebraically stabilized schemes for convection-diffusion-reaction problems, Numer. Math. 152 (2022), 553-585 download

  10. Knobloch, P.: A new algebraically stabilized method for convection-diffusion-reaction equations, in: F.J. Vermolen, C. Vuik (eds.), Numerical Mathematics and Advanced Applications ENUMATH 2019, Lecture Notes in Computational Science and Engineering 139, Springer-Verlag, Cham, 2021, pp. 605-613 download

  11. Knobloch, P., Lukáš, P., Solin, P.: Importance of parameter optimization in a nonlinear stabilized method adding a crosswind diffusion, J. Comput. Appl. Math. 393 (2021), Art. No. 113527, 8 pp. download

  12. Bodnár, T., Fraunié, Ph., Knobloch, P., Řezníček, H.: Numerical evaluation of artificial boundary condition for wall-bounded stably stratified flows, Discrete Contin. Dyn. Syst. Ser. S 14 (2021), 785-801 download

  13. John, V., Knobloch, P.: Existence of solutions of a finite element flux-corrected-transport scheme, Appl. Math. Lett. 115 (2021), Art. No. 106932, 6 pp. download

  14. John, V., Knobloch, P., Korsmeier, P.: On the solvability of the nonlinear problems in an algebraically stabilized finite element method for evolutionary transport-dominated equations, Math. Comp. 90 (2021), 595-611 download

  15. John, V., Knobloch, P., Wilbrandt, U.: Finite Element Pressure Stabilizations for Incompressible Flow Problems, in: T. Bodnár, G.P. Galdi, Š. Nečasová (eds.), Fluids Under Pressure, Advances in Mathematical Fluid Mechanics, Birkhäuser, Cham, 2020, pp. 483-573 download

  16. Knobloch, P., Lukáš, P., Solin, P.: On error indicators for optimizing parameters in stabilized methods, Adv. Comput. Math. 45 (2019), 1853-1862 download

  17. Brandner, M., Knobloch, P.: Some remarks concerning stabilization techniques for convection-diffusion problems, in: J. Chleboun, P. Kůs, P. Přikryl, M. Rozložník, K. Segeth, J. Šístek, T. Vejchodský (eds.), Programs and Algorithms of Numerical Mathematics 19, Institute of Mathematics, Czech Academy of Sciences, Prague, 2019, pp. 35-46 download

  18. Knobloch, P.: A linearity preserving algebraic flux correction scheme of upwind type satisfying the discrete maximum principle on arbitrary meshes, in: F.A. Radu, K. Kumar, I. Berre, J.M. Nordbotten, I.S. Pop (eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017, Lecture Notes in Computational Science and Engineering 126, Springer-Verlag, Cham, 2019, pp. 909-918 download

  19. John, V., Knobloch, P., Novo, J.: Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?, Comput. Visual. Sci. 19 (2018), 47-63 download

  20. Barrenechea, G.R., John, V., Knobloch, P., Rankin, R.: A unified analysis of algebraic flux correction schemes for convection-diffusion equations, SeMA J. 75 (2018), 655-685 download

  21. Dolejší, V., Knobloch, P.: Prof. Miloslav Feistauer seventy-fifth birthday celebration, Appl. Math. 63 (2018), 107-110 download

  22. Lukáš, P., Knobloch, P.: Adaptive techniques in SOLD methods, Appl. Math. Comput. 319 (2018), 24-30 download

  23. Dolejší, V., Knobloch, P.: Prof. Miloslav Feistauer oslaví 75. narozeniny, Pokroky matematiky, fyziky a astronomie 62 (2017), 300-302 download

  24. Knobloch, P.: On the discrete maximum principle for algebraic flux correction schemes with limiters of upwind type, Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016 (Z. Huang, M. Stynes, and Z. Zhang, eds.), Lect. Notes Comput. Sci. Eng., vol. 120, Springer, 2017, pp. 129-139 download

  25. Barrenechea, G.R., Knobloch, P.: Analysis of a group finite element formulation, Appl. Numer. Math. 118 (2017), 238-248 download

  26. Barrenechea, G.R., John, V., Knobloch, P.: An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes, Math. Models Methods Appl. Sci. 27 (2017), 525-548 download

  27. Bulling, J., John, V., Knobloch, P.: Isogeometric analysis for flows around a cylinder, Appl. Math. Lett. 63 (2017), 65-70 download

  28. Barrenechea, G.R., John, V., Knobloch, P.: Analysis of algebraic flux correction schemes, SIAM J. Numer. Anal. 54 (2016), 2427-2451 download

  29. Knobloch, P.: On the application of algebraic flux correction schemes to problems with non-vanishing right-hand side, In: Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014 (P. Knobloch - ed.), Lect. Notes Comput. Sci. Eng. 108, Springer-Verlag, 2015, pp. 99-109 download

  30. Barrenechea, G.R., John, V., Knobloch, P..: Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension, IMA J. Numer. Anal. 35 (2015), 1729-1756 download

  31. Knobloch, P.: Error estimates for a nonlinear local projection stabilization of transient convection-diffusion-reaction equations, Discrete Contin. Dyn. Syst. Ser. S 8 (2015), 901-911 download

  32. Barrenechea, G.R., John, V., Knobloch, P.: A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations, M2AN 47 (2013), 1335-1366 download

  33. Barrenechea, G.R., John, V., Knobloch, P..: A nonlinear local projection stabilization for convection-diffusion-reaction equations, Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011 (A. Cangiani, R.L. Davidchack, E. Georgoulis, A.N. Gorban, J. Levesley, M.V. Tretyakov - eds.), Springer-Verlag, Berlin, 2013, pp. 237-245 download

  34. John, V., Knobloch, P..: Adaptive computation of parameters in stabilized methods for convection-diffusion problems, Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011 (A. Cangiani, R.L. Davidchack, E. Georgoulis, A.N. Gorban, J. Levesley, M.V. Tretyakov - eds.), Springer-Verlag, Berlin, 2013, pp. 275-283 download

  35. Knobloch, P., Tobiska, L.: Improved stability and error analysis for a class of local projection stabilizations applied to the Oseen problem, Numer. Methods Partial Differential Equations 29 (2013), 206-225 download

  36. John, V., Knobloch, P., Savescu, S.B.: A posteriori optimization of parameters in stabilized methods for convection-diffusion problems - Part I, Comput. Methods Appl. Mech. Engrg. 200 (2011), 2916-2929 download

  37. Knobloch, P., Tobiska, L.: On the stability of finite element discretizations of convection-diffusion-reaction equations, IMA J. Numer. Anal. 31 (2011), 147-164 download

  38. Knobloch, P., Schütze, S., Tobiska, L.: Numerical treatment of a free surface problem in ferrohydrodynamics, PAMM 10 (2010), 573-574 download

  39. Knobloch, P.: Local projection method for convection-diffusion-reaction problems with projection spaces defined on overlapping sets, Numerical Mathematics and Advanced Applications 2009, Proceedings of ENUMATH 2009 (G. Kreiss, P. Lötstedt, A. Målqvist, M. Neytcheva - eds.), Springer-Verlag, Berlin, 2010, pp. 497-505 download

  40. Knobloch, P.: A generalization of the local projection stabilization for convection-diffusion-reaction equations, SIAM J. Numer. Anal. 48 (2010), 659-680 download

  41. Knobloch, P.: Numerical solution of convection-diffusion equations using a nonlinear method of upwind type, J. Sci. Comput. 43 (2010), 454-470 download

  42. Knobloch, P.: On a variant of the local projection method stable in the SUPG norm, Kybernetika 45 (2009), 634-645 download

  43. Knobloch, P.: On the choice of the SUPG parameter at outflow boundary layers, Adv. Comput. Math. 31 (2009), 369-389 download

  44. Knobloch, P., Lube, G.: Local projection stabilization for advection-diffusion-reaction problems: One-level vs. two-level approach, Appl. Numer. Math. 59 (2009), 2891-2907 download

  45. Knobloch, P.: On the application of local projection methods to convection-diffusion-reaction problems. In: BAIL 2008 - Boundary and Interior Layers (A. F. Hegarty, N. Kopteva, E. O' Riordan, M. Stynes - eds.), Lect. Notes Comput. Sci. Eng. 69, Springer-Verlag, Berlin, 2009, pp. 183-194 download

  46. Knobloch, P.: On the definition of the SUPG parameter, Electron. Trans. Numer. Anal. 32 (2008), 76-89 download

  47. John, V., Knobloch, P.: On the choice of parameters in stabilization methods for convection-diffusion equations. In: Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2007 (K. Kunisch, G. Of, O. Steinbach - eds.), Springer-Verlag, Berlin, 2008, pp. 297-304 download

  48. John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: Part II - Analysis for P1 and Q1 finite elements, Comput. Methods Appl. Mech. Engrg. 197 (2008), 1997-2014 download

  49. John, V., Knobloch, P.: On the performance of SOLD methods for convection-diffusion problems with interior layers, Int. J. Comput. Sci. Math. 1 (2007), 245-258 download

  50. Knobloch, P.: Application of the Mizukami-Hughes method to bilinear finite elements, Proceedings of Czech-Japanese Seminar in Applied Mathematics 2006, COE Lecture Note Vol. 6, Faculty of Mathematics, Kyushu University, 2007, pp. 137-147

  51. John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: Part I - A review, Comput. Methods Appl. Mech. Engrg. 196 (2007), 2197-2215 download

  52. John, V., Knobloch, P.: A computational comparison of methods diminishing spurious oscillations in finite element solutions of convection-diffusion equations. In: J. Chleboun, K. Segeth, T. Vejchodský (eds.), Proceedings of the International Conference Programs and Algorithms of Numerical Mathematics 13, Academy of Science of the Czech Republic, Prague, 2006, pp. 122-136 download

  53. Knobloch, P., Šedivý, P.: Numerical simulation of the free fall of a rigid body in a viscous fluid, Proceedings of the XVIth Summer School Software and Algorithms of Numerical Mathematics, University of West Bohemia, Pilsen, 2006, pp. 108-117. download

  54. John, V., Knobloch, P.: On discontinuity-capturing methods for convection-diffusion equations. In: Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2005 (A. Bermúdez de Castro, D. Gómez, P. Quintela, P. Salgado - eds.), Springer-Verlag, Berlin, 2006, pp. 336-344. download

  55. Knobloch, P.: Numerical solution of convection-diffusion equations using upwinding techniques satisfying the discrete maximum principle, Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005, COE Lecture Note Vol. 3, Faculty of Mathematics, Kyushu University, 2006, pp. 69-76. download

  56. Knobloch, P.: Improvements of the Mizukami-Hughes method for convection-diffusion equations, Comput. Methods Appl. Mech. Engrg. 196 (2006), 579-594. download

  57. Knobloch, P.: On stability of the $P_n^{mod}/P_n$ element for incompressible flow problems, Appl. Math. 51 (2006), 473-493. download

  58. Knobloch, P.: Reduced finite element discretizations of the Stokes and Navier-Stokes equations, Numer. Funct. Anal. and Optimiz. 27 (2006), 161-187. download

  59. Knobloch, P.: On the inf-sup condition for the $P_3^{mod}/P_2^{disc}$ element, Computing 76 (2006), 41-54. download

  60. Knobloch, P., Tobiska, L.: On Korn's first inequality for quadrilateral nonconforming finite elements of first order approximation properties, Int. J. Numer. Anal. Model. 2 (2005), 439-458. download

  61. Knobloch, P.: Influence of mesh-dependent Korn's inequality on the convergence of nonconforming finite element schemes, in Proceedings of Czech-Japanese Seminar in Applied Mathematics 2004, M. Beneš, J. Mikyška, and T. Oberhuber, eds., Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, 2005, pp. 85-95. download

  62. Knobloch, P.: On the application of the $P_1^{mod}$ element to incompressible flow problems, Comput. Visual. Sci. 6 (2004), 185-195. download

  63. Knobloch, P., Tobiska, L.: The $P_1^{mod}$ element: a new nonconforming finite element for convection-diffusion problems, SIAM J. Numer. Anal. 41 (2003), 436-456. download

  64. Knobloch, P.: New nonconforming finite elements for solving the incompressible Navier-Stokes equations. In: Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2001 (F. Brezzi, A. Buffa, S. Corsaro, A. Murli - eds.), Springer-Verlag, Milano, 2003, pp. 123-132. download

  65. John, V., Knobloch, P.: On non-nested multilevel solvers for the Stokes and Navier-Stokes equations. In: W. Hackbusch, M. Griebel (Eds.), Multigrid and Related Methods for Optimization Problems, MPI MIS, Leipzig, 2002, pp. 77-95. download

  66. Knobloch, P.: Nonconforming finite elements for incompressible flow problems, Proceedings of the XIVth Summer School Software and Algorithms of Numerical Mathematics, University of West Bohemia, Pilsen, 2002, pp. 123-145. download

  67. John, V., Knobloch, P., Matthies, G., Tobiska, L.: Non-nested multi-level solvers for finite element discretisations of mixed problems, Computing 68 (2002), 313-341. download

  68. Knobloch, P.: On some nonconforming finite elements for incompressible flow problems. In: K. Kozel, J. Příhoda, M. Feistauer (Eds.), Proceedings of 4th Seminar on Euler and Navier-Stokes Equations (Theory, Numerical Solution, Applications), Institute of Thermomechanics AS CR, 2001, 61-64. download

  69. Knobloch, P.: On the validity of discrete Korn's inequality for nonconforming finite element spaces. In: Numerical Modelling in Continuum Mechanics, Proceedings of the 4th Summer Conference held in Prague, 31 July - 4 August, 2000 (M. Feistauer, R. Rannacher, K. Kozel - eds.), MatfyzPress, Praha, 2001, 191-199. download

  70. Knobloch, P.: Uniform validity of discrete Friedrichs' inequality for general nonconforming finite element spaces, Numer. Funct. Anal. and Optimiz. 22 (2001), 107-126. download

  71. Knobloch, P., Tobiska, L.: On bubble-based modifications of the nonconforming $P_1$ element for solving convection-diffusion equations, CD-Rom Proceedings of ECCOMAS 2000 (European Congress on Computational Methods in Applied Sciences and Engineering) held in Barcelona, September 11-14, 2000, ed. by E. Oñate, G. Bugeda and B. Suárez, FIB, CIMNE, Barcelona, 2000, 1-20. download

  72. Knobloch, P.: On Korn's inequality for nonconforming finite elements, Technische Mechanik 20 (2000), 205-214 and 375 (errata). download

  73. Knobloch, P., Tobiska, L.: Modified FE discretizations of incompressible flow problems and their relationship to stabilized methods, Proceedings of the 3rd European Conference Numerical Mathematics and Advanced Applications, ed. by P. Neittaanmäki, T. Tiihonen and P. Tarvainen, World Scientific, Singapore, 2000, pp. 571-578. download

  74. Knobloch, P., Tobiska, L.: A bubble-type stabilization of the $Q_1/Q_1$-element for incompressible flows. In: Partial differential equations, Theory and numerical solution (W. Jäger, J. Nečas, O. John, K. Najzar, J. Stará - eds.), Research Notes in Mathematics 406, Chapman & Hall/CRC, Boca Raton, 2000, pp. 230-239. download

  75. Knobloch, P.: A finite element convergence analysis for 3D Stokes equations in case of variational crimes, Appl. Math. 45 (2000), 99-129. download

  76. Knobloch, P., Tobiska, L.: Stabilization methods of bubble type for the $Q_1/Q_1$- element applied to the incompressible Navier-Stokes equations, M2AN 34 (2000), 85-107. download

  77. Knobloch, P.: Variational crimes in a finite element discretization of 3D Stokes equations with nonstandard boundary conditions, East-West J. Numer. Math. 7 (1999), 133-158. download

  78. Knobloch, P., Tobiska, L.: A streamline diffusion method for nonconforming finite element approximations applied to the linearized incompressible Navier-Stokes equation, Recent Advances in Numerical Methods and Applications II, O. P. Iliev, M. S. Kaschiev, S. D. Margenov, B. H. Sendov and P. S. Vassilevski eds., Proceedings of the Fourth International Conference, NMA'98, Sofia, Bulgaria, 19-23 August 1998, World Scientific, Singapore, 1999, pp. 530-538. download

  79. Knobloch, P., Tobiska, L.: Analysis of a mathematical model related to Czochralski crystal growth, Abstr. Appl. Anal. 3 (1998), 319-342. download

  80. Knobloch, P., Tobiska, L.: Stabilization of finite element discretizations of the Stokes and Navier-Stokes equations with respect to the Reynolds number. In: K. Kozel, J. Příhoda, M. Feistauer (Eds.), Proceedings of 3rd Seminar on Euler and Navier-Stokes Equations (Theory, Numerical Solution, Applications), Institute of Thermomechanics AS CR, 1998, 51-52.

  81. Knobloch, P., Tobiska, L.: A new approach to derive stable discretizations of the Stokes and Navier-Stokes equations. In: ENUMATH 97, Proceedings of the 2nd European Conference on Numerical Mathematics and Advanced Applications (H. G. Bock, G. Kanschat, R. Rannacher, F. Brezzi, R. Glowinski, Y. A. Kuznetsov, J. Periaux - eds.), World Scientific, Singapore, 1998, 413-420. download

  82. Knobloch, P.: Treatment of variational crimes in discretizations of three-dimensional Navier-Stokes equations. In: Numerical Modelling in Continuum Mechanics, Proceedings of the 3rd Summer Conference held in Prague, 8-11 September, 1997 (M. Feistauer, R. Rannacher, K. Kozel - eds.), MatfyzPress, Praha, 1997, 344-352. download

  83. Knobloch, P., Tobiska, L.: Modelling of 3D melt flow in Czochralski crystal growth. In: Algoritmy '97, Proceedings of 14th Conference on Scientific Computing held in West Tatra Mountains - Zuberec, Slovakia, September 2-5, 1997 (A. Handlovičová, M. Komorníková, K. Mikula - eds.), Slovak Technical University, Bratislava, 1997, 78-88. download

  84. Knobloch, P.: Discrete Friedrichs' and Korn's inequalities in two and three dimensions, East-West J. Numer. Math. 4 (1996), 35-51. download

  85. Knobloch, P.: Finite element analysis of a three-dimensional melt flow model including treatment of variational crimes. In: K. Kozel, J. Příhoda (Eds.), Proceedings of 2nd Seminar on Euler and Navier-Stokes Equations (Theory, Numerical Solution, Applications), Institute of Thermomechanics AS CR, 1996, 33-34.

  86. Knobloch, P.: Weak solvability of a model related to crystal growth processes. In: Numerical Modelling in Continuum Mechanics, Proceedings of the 2nd Summer Conference held in Prague, August 22-25, 1994 (M. Feistauer, R. Rannacher, K. Kozel - eds.), Faculty of Mathematics and Physics, Charles University, Prague, 1995, 162-170.

  87. Feistauer, M., Knobloch, P.: Operator splitting method for compressible Euler and Navier-Stokes equations. In: Numerical Methods for the Navier-Stokes Equations. Notes on Numerical Fluid Mechanics, Vol. 47 (F.-K. Hebeker, R. Rannacher, G. Wittum - eds.), Vieweg, Braunschweig - Wiesbaden, 1994, 70-78.

  88. Feistauer, M., Medviďová, M., Knobloch, P.: Finite Element - Finite Volume Operator Splitting Method for Compressible Euler and Navier-Stokes Equations. In: Proceedings of the Colloquium Fluid Dynamics 1993, Institute of Thermodynamics, Czech Academy of Sciences, Prague, 1993, 9-10.
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