Petr Knobloch


Research interests

Publications

Curriculum vitae

Teaching


List of publications

  • 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, Preprint No. MATH-knm-2007/4, Charles University, Faculty of Mathematics and Physics, Prague, 2007 download

  • Knobloch, P.: On the choice of the SUPG parameter at outflow boundary layers, Preprint No. MATH-knm-2007/3, Charles University, Faculty of Mathematics and Physics, Prague, 2007 download

  • 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 preprint

  • 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

  • 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

  • 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

  • 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

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

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

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

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

  • 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

  • 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

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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

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

  • 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

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

  • 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

  • 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

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

  • 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

  • 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

  • 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

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

  • 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.

  • 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

  • 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

  • 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

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

  • 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.

  • 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.

  • 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.

  • 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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